International Encyclopedia of Statistical Science

Miodrag Lovric (Ed.) International Encyclopedia of Statistical Science

With  Figures and  Tables

123 Editor: Miodrag Lovric Department of Statistics and Informatics Faculty of Economics University of Kragujevac City of Kragujevac Serbia

Library of Congress Control Number: 

ISBN ---- This publication is available also as: Electronic publication under ISBN ---- Print and electronic bundle under ISBN ---- DOI ./----

Springer Heidelberg Dordrecht London New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September , , in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law.

© Springer-Verlag Berlin Heidelberg 

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Springer is part of Springer Science+Business Media www.springer.com

Printed on acid-free paper SPIN:  Spi–

Foreword by Bradley Efron The Future of Statistics

▸ Strange, as one gets older you’re expected to know and  columns, one for each man: enormous by Twenti- more about the future. eth Century standards but nothing remarkable these days. We wonder which of the genes, if any, are more active in The history of statistics as a recognized discipline divides the cancer patients. rather neatly at , the year of Karl Pearson’s chi-square As a first step we can compute a two-sample t-statistic paper. Before then we are still close to the world of t comparing expression levels between cancer patients and Quetelet, where huge census-level data sets are brought to i controls on gene i.ForFig. ,eacht has been transformed bear on simple but important questions: Are there more i into a z-value z , by definition a test statistic having a stan- male or female births? Is the murder rate rising? Then, i dard normal distribution under the null hypothesis that as if on cue, the Twentieth Century rings in a focus on gene i behaves the same in both groups, small-scale statistics. A team of intellectual giants, Fisher,

Neyman, Hotelling, …, invent a theory of optimal infer- H : zi ∼N(, ).() ence, capable of wringing out every drop of collected N( ) information. The questions are still simple: Is treatment A The histogram of the  zi’s looks like a ,  curve better than treatment B? But the new methods are suited near its center, which makes sense since presumably most to the kinds of small data sets an individual scientist might of the genes are not involved in prostate cancer etiology, collect. but it also shows a promising excess of values in the What does this have to do with the future of statistics? extreme tails. For example,  of the zi’s exceed  (indi- Quite a bit, perhaps: the Twenty-First Century, again on cated by the hash marks) whereas the expected number is cue, seems to have initiated a third statistical era. New tech- only . if all the genes follow (). Should we report the list nologies, exemplified by the microarray, permit scientists of  back to the researchers as interesting candidates for to collect their own huge data sets. But this is not a return to further study? the age of Quetelet. The flood of data is now accompanied Any one of the genes is wildly significant by classical > by a flood of questions, perhaps thousands of them, that single-test standards where we would reject H for zi = the statistician is charged with answering together; not at ., the two-sided . value. But with N , , the . > / all the setting Fisher et al. had in mind. Bonferroni bound requires zi ., the two-sided . N As a cruder summary of my already crude statistical value, and only  of the  genes make the cut. history, we have In what might be taken as a premonitory salvo of Twenty-First Century statistics, Benjamini and Hochberg th Century: Large data sets, simple questions () proposed a different, more lenient standard for th Century: Small data sets, simple questions large-scale testing based on False Discovery Rates: st Century: Large data sets, complex questions Fdr()=./ = . () The future of statistics, or at least the next large chunk of future, will be preoccupied, I believe, with problems of in our case, the ratio of counts expected under null con- large-scale inference raised in our revolutionary scientific ditions to those actually observed in the interval (, ∞). environment. For example, how should one analyze ,  Assuming independence of the z-values, they showed that related hypothesis tests or ,  correlated estimates at a statistician who chooses to reject all zi’s in the largest thesametime? interval (x, ∞) such that Fdr(x) is less than some control Figure  concerns an example of large-scale inference level q will make an expected proportion of false discover- from Singh et al. ():  prostate cancer patients and  ies no greater than q.Takingq = . for the prostate data normal controls have each had his genetic expression levels gives x =  and suggests that /ofthelistofarefalse measured on N = ,  genes. This produces a matrix of discoveries, the other / being genuinely non-null genes: measurements X with N = ,  rows, one for each gene, not bad odds for the prospects of further investigation. viii Foreword by Bradley Efron

200 N(0,1)

150

100 Frequency

50 49 z-values exceed 3

0

−4 −2 0 2 4

Figure  N = , z-values, prostate study

Controlling Fdr is fundamentally different than con- that a randomly selected zi, null or not, exceeds x. trolling the probability of Type I error. Now the signifi- Substituting the empirical cdf Fˆ(x) for the unknown cance of a gene that has zi >  depends on how many F(x) gets us back to definition (); see Efron (). others exceed . If there were only  such, instead of , We can restate the Benjamini–Hochberg procedure in we would have Fdr()=.; not an encouraging prospect Bayesian terms: “Reject those zi’s in the largest interval for the investigators. (x, ∞) that has estimated Bayes null probability ()less Twentieth Century applied statistics has been very than q.” much a world of direct evidence in which each case, each Indirect evidence is not the sole property of Bayesians. gene in our example, is judged entirely on its own data. This Tukey’s phrase “borrowing strength” nicely captures the is a world designed for frequentism, where objectivity is frequentist regression tactic of using nearby data points enforced by notions of unbiasedness, minimum variance, to assist in estimation at a particular point of interest. size and power. But large-scale data sets like that for the “Nearby” refers to distance in a space of relevant covari- prostate study abound with indirect evidence: our inter- ates. The explosion in data collection has brought with it est in zi is affected by all the other zj’s. I believe that the an explosion in the number of covariates, often too many immediate future of statistical theory and practice crucially for standard regression techniques. A thriving industry of involves “learning from the experience of others,” i.e., the new methods has emerged – boosting, bagging, CART, incorporation of indirect evidence. Lasso, LARS, projection pursuit – which search to build Bayes theorem is a perfect recipe for learning from the effective regression models from subsets of the available experience of others, and we can expect Bayesian meth- regressors. The generic term here is data mining,which ods to play a greater role in Twenty-First Century data beganasaninsultbutnowseemstohaveitsownrobust analysis. Fdr theory was derived frequentistically, but it statistical future. has a compelling Bayesian rationale. Assuming that the Bayesian and frequentist ideas are combined happily in prior probability of a null case is near , Bayes theorem the Fdr algorithm. Other lines are blurred too: in ()we yields are estimating the hypothesis testing quantity (); that is, we are carrying out an “empirical Bayes” analysis, to use Pr{gene i is null∣z ≥ x}≐F (x)/F(x) () i  Robbins’ apt description. Blurred lines are another likely

where F is the probability that a null zi exceeds x [equal- (and hopeful) trend, as Twenty-First Century statisticians ing  − Φ(x) under ()] and F(x) is the probability outgrow the confines of classical theory. Foreword by Bradley Efron ix

In moving beyond the classical confines we are also to show that expected effect size μ(z) is a simple function moving outside its wall of protection. Fisher, Neyman et al. of f (z), fashioned, with enormous intellectual effort, an almost d μ(z)=z + log f (z).() perfect inferential machine for small-scale estimation and dz testing problems. It took our brilliant predecessors at least The heavy curve in Fig.  is an empirical Bayes estimate  years to work the kinks out of ANOVA/linear model of (): a smooth curve fˆ(z) was fit to the heights of the theory. My guess is for another long period of progress histogram bars in Fig.  and its logarithm differentiated to and retrenchment. Difficulties with large-scale inference give μˆ(z);seeEfron(). Gene  has z = ., the are easy to find. Not all microarray data sets are as oblig- largest of the  z-values, with effect size estimate μˆ = ing as that from the prostate study. Often the histogram ., as indicated. ismuchwiderornarrowerthaninFig. ,castinggrave We can be almost certain that z,asthemaximumof doubt on the adequacy of the textbook null hypothesis N = ,  observations, exaggerates μ. This is the curse (). Correlations sprawl across the z-values, undermining of selection bias. Bayes estimates, according to theory, are accuracy of the empirical Bayes estimator. Effect sizes for immune to selection bias: if μˆ were a genuine Bayes the genes deemed “non-null” are difficult to assess because posterior estimate of μ, we would not have to concern of massive selection biases from choosing among so many ourselves that gene  was selected on the basis of the data. candidates. Et cetera, et cetera. In other words, there is a lot A Bayes prior effectively postulates an infinite amount of for statisticians to think about over the next  years. relevant past experience, swamping selection effects from Some of that thinking will involve the legitimate use mere thousands of observations. of Bayesian methods in large-scale inference. As an exam- Are empirical Bayes estimates immune to selection ple, Fig.  concerns effect size estimation in the prostate bias? N = ,  is not N = infinity, and we might sus- study. Suppose that the z-value for gene i follows a normal pect at least some selection effects to linger in μˆ.Other distribution, very appealing Bayesian properties, like the right to take ∼N( ) zi μi, ,()interim looks at a clinical trial without an optional stop- μi the “effect size” (so μi =  for the null genes ()), where ping penalty, are not put to the test in small-scale situ- the effect sizes are drawn from some unknown Bayesian ations. Large-scale studies offer their own self-contained prior distribution G(μ).Callf (z) the marginal density of universes in which it may be possible to settle such z-values induced by G(μ) and (). Then it is not difficult questions.

4 4.11

2

0 5.29 Effect size estimate –2

–4 Observed value z−>

–4 –2 0246

Figure  Effect size estimates for prostate study x Foreword by Bradley Efron

Statistics is a second-level science: our “nature” is the Loda M, Kantoff PW, Golub TR, Sellers WR () Gene expres- data-analytic questions posed by front-line scientists – sion correlates of clinical prostate cancer behavior. Cancer Cell biologists, astronomers, economists, etc. – the “etc.” by :– now spanning almost all areas of quantitative inquiry. The Bradley Efron future of statistics depends on the future of science, in par- Max H. Stein Professor of Statistics and Biostatistics ticular of scientific technology. There’s a good chance that Stanford University today’s huge data sets will seem puny in a few years, in Stanford, CA which case this little essay will look remarkably timid. USA The future I’ve been discussing is that of statistics as an intellectual discipline. What about the future of [Past President, American Statistical Association the statistics profession? There is no question that the (), Past President, Institute of Mathematical Statis- probabilistic/statistical point of view continues its relent- tics (–), Founding Editor, The Annals of Applied less spread across science and engineering. (Maybe scien- Statistics (–), Bradley Efron, is considered as “one tists are just running out of problems simple enough to of the most innovative and original contributors to sta- solve deterministically.) So there will be more people inter- tistical science today” (StatNews, Penn State, December ested in statistical questions, but that doesn’t necessarily ). He is the Max H. Stein Professor of Statistics and imply more statisticians. The field could fractionate into Biostatistics at Stanford University’s School of Humani- subject area subspecialties. ties and Sciences and the Department of Health Research I don’t think so. The health of a scientific profession can and Policy with the School of Medicine, USA. Professor be rated on three criteria: Efron is member of American Academy of Arts and Sci- ● An outside demand for answers in the profession’s ences () and National Academy of Sciences (). He chosen area. has been awarded the Ford Prize, Mathematical Associ- ● Some evidence of past success in answering such ques- ation of America (), MacArthur award (), Wilks tions. Medal, American Statistical Association (August ), ● An ongoing production of useful new ideas. Fisher Prize, Committee of Presidents of Statistical Soci- eties (July ), Parzen Prize for Statistical Innovation, In other words, the profession should be healthy from both Texas A&M University (), the first-ever C.R. & Bhar- an inside and outside point of view. I give statistics high gavi Rao Prize (), Noether Prize, American Statistical grades on all three criteria, perhaps higher than at any time Association (). On May , , he was awarded the in the past half-century. In one sense we have a monopoly: National Medal of Science, the highest scientific honor by statistics is the only profession that takes applied inference the United States “for his contributions to theoretical and seriously as a subject of study. So in my view, our future applied statistics, especially the bootstrap sampling tech- workiscutoutforus,butit’snotcutoutforanyoneelse. nique; for his extraordinary geometric insight into nonlin- References ear statistical problems; and for applications in medicine, Benjamini Y, Hochberg Y () Controlling the false discovery rate: physics, and astronomy.” a practical and powerful approach to multiple testing. J Roy “Brad Efron is renowned as a quintessential, theoretical, Statist Soc Ser B :– mathematical, interdisciplinary, and applied statistician. Efron B () Microarrays, empirical Bayes and the two-groups His foreseeing the onset of cheap and fast computation model. Statist Sci :– inspired his most famous breakthrough in , the ‘boot- Efron B () Empirical Bayes estimates for large-scale prediction problems. J Am Statist Assoc :– strap’, which marks the onset of the computer intensive age Singh D, Febbo PG, Ross K, Jackson DG, Manola J, Ladd C, in statistics.” (Professor Carl Morris, Harvard University, Tamayo P, Renshaw AA, D’Amico AV, Richie JP, Lander ES, Notices of the AMS, , p. ).] Foreword by Rajko Kuzmanovic´

▸ Inventas vitam iuvat excoluisse per artes Vergil In the Republic of Srpska, and in Bosnia and Herzegovina, we need to encourage statistics both as a science and as an aid to developing the economy of our region. This Encyclopedia goes a significant way towards meeting that challenge. It provides us with international visibility in statistics, it demonstrates our unity, energy and judgement, and it shows our capacity for collaboration. However, the Encyclopedia does much more than that. This storehouse of the knowledge and wisdom of statisticians from around the world displays the unity of the broad international statistics community, and provides a resource of substantial scientific benefit to all nations. It demystifies the concepts and philosophy of statistics, not just to students and researchers in the field but to their many non-statistician colleagues in other areas, who need to understand statistics in order to make progress in their own disciplines. As the historian Theodore Porter wrote, “statistics . . . is evidently among theproductsofsciencewhoseinfluenceonpublicandprivatelifehasbeenmostpervasive.” For all these reasons we believe that the Encyclopedia will become the starting point for still further development of scientific knowledge, and be of influence for many years to come. At least in our region we feel that time, in the statistics community, will henceforth be designated as BE or AE — before the Encyclopedia,orafterit. Speaking personally, it is with unconcealed pride in this achievement that I take this opportunity to express my great satisfaction with the project, and my deep gratitude to the scientists and scholars who have contributed so generously to it. I believe that the Encyclopedia will inspire a younger generation of statistical scientists to study and dedicate themselves to the discipline. It will draw them closer to researchers in many other fields, and closer too to their colleagues in other nations.

President Academy of Sciences and Arts Republic of Srpska

Academician Rajko Kuzmanovic,´ Ph.D.

Preface

▸ Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. Samuel Wilks (paraphrasing Herbert G. Wells) ▸ The quiet statisticians have changed our world—not by discovering new facts or technical developments, but by changing the ways we reason, experiment and form our opinions about it. Ian Hacking, Contemporary Philosopher

Why is there a need for one more encyclopedia and what is so special and unique with the book that you have just started reading? After perusing the prefaces to at least  encyclopedias, I can provide  distinctive arguments and answers: . As you will see more in the next section the main objective of this project, help reviving statistics education in developing countries, is very different and broader and has a valuable social dimension. This goal has attracted and united many leading world statisticians, four Nobel Laureates, many eminent mathematicians, psychologists, philosophers, econometricians, economists, academicians, Presidents and founders of Statistical societies, and Editors and Associate Editors of many reputed international journals, who have decided to participate. . One of the hallmarks of the Encyclopedia is its international scope, it has  contributors from  countries making this assignment one of the largest international scientific projects ever undertaken (from the perspective of the number of countries involved), not only in Statistics, but also in other branches of Science. We have shown that statistical science does not recognize and cares for country borders and customs; this united world effort encompasses countries that overall include more than % of the world population altogether, in a way we have fulfilled John Lennon’s dream: “and the world will be as one”. . Many of our papers have resulted as collaborations of authors coming from different countries, for example we have a paper written by authors from USA and Russia, paper by authors from USA, Philippines and Spain; from Serbia and Croatia; Australia, UK and Switzerland, to mention a few. . For the first time authors from many developing countries have had an opportunity to work together on the same project with the leading world authorities in statistics and quantitative methods. . Almost all leading experts from many developing countries have been involved, including presidents of their statistical societies. This encyclopedia has contributors from almost all countries in the world that have statistics departments or professors in statistics; . Many papers from this encyclopedia have been selected to provide the backbone of StatProb,thefree online encyclopedia of statistics, sponsored by statistics and probability societies (http://statprob.com). . This project has several contributors whose papers can be regarded as conveying an encouraging and mesmerizing message “never say never” to all of us, for example one author has been blind since  and yet provided a paper with many formulas, several most distinguished authors are over  and one is even  years old. . In contrast to almost all other encyclopedias, this one includes achievement biographies of many contributed authors. . To overcome pervasive stereotyped public images that Statistics is dull and boring, I invited many authors to write non-standard papers with our joint vision: to show not only that Statistics is a “grammar of science”,but also a fascinat- ing, attractive, stimulating, beautiful, almost magical discipline with plenty of room for fundamental improvements. For example, instead of standard foreword, Professor Bradley Efron has given his vision on the future of statistics. Former President of the American Statistical Association, Jon R. Kettenring, has written the paper on “The Rise of Statistics in the Twenty First Century” mentioning the headline that appeared on the front page of The New York Times: “For today’s graduate, just one word: statistics.” Professor Shlomo Sawilowsky has written a paper “Statisti- cal Fallacies, Misconceptions, and Myths”, Professor Jan Kmenta “Econometrics: a failed science?”, Professor Jagdish xiv Preface

Srivastava “Clinical Trials: Some Aspects Of Public Interest”,Professor William Notz “Statistics - Resolving Contro- versies In Practice”, Professors Bruno Lecoutre and Shlomo Sawilowsky contrast their views on hypothesis testing, and Professors John Nelder and Herman Rubin give their different views on statistics, etc. . This encyclopedia includes last papers and words written by four eminent statisticians who had made great contribution to our science.

The Origin of the Encyclopedia and Its Goal This project started to correct the lacuna in Statistics education in Macedonia, Serbia, Montenegro and Bosnia that were once part of former Yugoslavia. After long discussions, an Organizational Committee was formed for writing and pro- moting a Dictionary of Statistics and as many such dictionaries were on the market, the title was changed to Lexicon of Statistics. The Organizational Committee was structured such that from each of the former Yugoslavian republics (except Monte Negro) a president was elected (in alphabetical order): Bosnia: Professor Jasmin Komic´ (also the President of the Committee), Croatia: Professor Ksenija Dumiciˇ c´, Macedonia: Professor Kalina Trenevska Blagoeva, Serbia: Professor Milan Merkle and Slovenia: Professor Jože Rovan. Initially, the idea was to invite only the statisticians from the former Yugoslavian republics. It had been regarded as a significant success to realize a project with authors coming from all these republics, for the first time after the “third Balkan war”. The choice of the language was very difficult because of the different dialects (languages), and finallywe decided to select English as the official Lexicon language. Later, some of the eminent statisticians and professors (in chronological order) Peter Hall, BradleyEfron, James Hamilton, Robert Tibshirani, DavidMoore, Ronald Iman, Peter Diggle and E.L. Lehmann have submitted brief definitions of some statistical terms. However, a few like Thomas Hettmansperger, Peter Kennedy, Geert Molenberghs, Hirotogu Akaike and Alan Agresti submitted brief articles. This reshaped my vision to strive for brief articles rather than definitions. Sir David Cox who pointed to some important statisticians in Europe provided the major impetus for this idea. In preparing for this expanded project the committee realized that Statistics education is also on the decline in many developing countries. After I exchanged more than  emails with statisticians from all over the world, the scope of the project was further broadened to revive interest in Statistics in developing countries.Theresponsewasso unprecedented and unbelievable that the title of this project was changed from Lexicon of Statistics into International Encyclopedia of Statistical Science. I have decided to include the Lexicon part and the interested reader can find it in the volume . All the contributors have committed themselves to giving our readers the best, despite the imperfections that inhere in any human endeavor. We hope that those who use this encyclopedia experience the pleasure and insight that we have worked to provide. If this united world effort ignite a spark of enthusiasm about statistics and henceforth revitalize interest in statistics education in developing countries and also inspire many high school students to study statistics we will consider mission fulfilled. Finally, I should mention that during this process, four of our esteemed contributors have passed away, Professor Hirotugu Akaike, Nobel Laureate Sir Clive Granger,ProfessorErich Lehmann and Professor John Nelder.Eachof these figures have made considerable contributions to our discipline, and will be sadly missed. I feel it appropriate to dedicate the Encyclopedia to their memory.

List of Articles by the Reader’s Background This encyclopedia has  entries arranged in alphabetical order. There are many co-authored papers and at the same time many authors have written two or more papers, Professor Sander Greenland even nine. The Encyclopedia includes extensive cross-referencing of two types: inline (included within a body of a paper) and “external” (provided at the end of the entry). Responsibility for these cross-references lies ultimately with me, though I am thankful to those authors who Preface xv have suggested cross-references for their own papers. This work was designed to provide useful up-to-date trustworthy information, including the latest advances in statistics, for different categories of users: High school students (they are strongly advised to read the papers “Statistics: An Overview”, “Careers in Statistics”, “Rise of Statistics in the Twenty First Century”, “Statistics: Nelder’s view” and the “Role of Statistics”, among others). Undergraduate students in almost any field (they can start reading this encyclopedia by finding the paper onthe relation of statistics and their particular field of study). Businesspersons (they can find valuable information in the following entries, among others,: “Business Forecasting Methods”, “Forecasting Principles”, “Business Statistics”, “Economic Statistics”, “Detection of Turning Points in Business Cycles”,“Business Intelligence”,“Data Mining” and “Business Surveys”). Researchers in all branches of science (they are urged to start reading the following entries: “Research Designs”,“Statis- tical Significance”,“Statistical Evidence”,“Null-Hypothesis Significance Testing: Misconceptions”, “Effect Size”,“P-Values”, “Bayesian Versus Frequentist Statistical Reasoning”,“Statistical Fallacies: Misconceptions, and Myths”,“Significance Tests: A Critique” and “Frequentist Hypothesis Testing: A Defense”). Authors of the introductory university statistics textbooks (they could start by reading the following entries: “Statistics: An Overview”,“Statistical Literacy, Reasoning, and Thinking”,“Statistical Inference: An Overview”,“Bayesian Versus Fre- quentist Statistical Reasoning,” “Bayesian Statistics”, “Psychology, Statistics in”,“Misuse of Statistics”,“Statistical Fallacies: Misconceptions, and Myths”, “Statistics: Controversies in Practice”, “Null-Hypothesis Significance Testing: Misconcep- tions”,“Effect Size”,“Role of Statistics”,“Statistics Education”,“Data Mining”,“Online Statistics Education”,“Measurement Scales And Choice Of Statistical Method”, “Harmonic Mean”, “Sturges’ and Scott’s Rules”, “Skewness”, and “Significance Testing: An Overview”.They will certainly find a wealth of information and many issues that they could cover or amend in their future editions, and many new angles on all those topics, that they could not find in standard textbooks). All other readers can start using the encyclopedia by reading the entries “Statistics: An Overview”, “Clinical Trials: Some Aspects of Public Interest”,or “Rise of Statistics in the Twenty First Century”. We believe that any non-statistician will be able to obtain quick and yet comprehensive and highly understandable view on certain statistical terms, methods or applications. Additionally, we trust that all researchers, managers and practitioners will regard this encyclopedia as a highly valuable resource that will help them refreshing their knowledge in Statistics, especially in certain controversial fields.

Acknowledgments I would like to express my profound thanks to all our contributors who have made substantial and Herculean efforts and devoted their valuable time to support this project. This is neither a Serbian nor a Yugoslavian Encyclopedia, but a joint work of many leading statisticians, economists, philosophers, engineers, sociologists, econometricians, psychologists and other scientists from all over the world, and is truly a World Encyclopedia. Throughout the progress of this work almost all authors have given many invaluable ideas to improve some entries and to include other topics, or suggestions to invite other eminent scholar. The Ministry of Science of the Republic of Srpska, Rajko Kuzmanovic´, President (–), Milorad Dodik, Prime Minister (–, now President) and the University of Banja Luka accorded formal recognition to this project and helped me substantially to complete it. I would also like to especially thank Presidents and Past Presidents of many statistical associations for their support and contributed papers, including the ones from the following countries (alphabetically): Argentina, Armenia, Austria, Belarus, Belgium, Brazil, Canada, Chile, China, Estonia, Germany, Hong Kong, India, Ireland, Israel, Italy, Japan, Korea, Kyrgyzstan, Mexico, Nepal, New Zealand, Palestine, Saudi Arabia, Slovenia, South Africa, Sweden, The Netherlands, Turkey, Uganda, UK, and USA; I am indebted to Presidents, Past Presidents, Directors and Chairmen of many reputed international scientific organi- zations for their decisions to take part in this project, including: Academy of Marketing Science, African Centre for Statistics, Bachelier Finance Society, Bernoulli Society, European Consortium for Mathematics in Industry, European Consortium of Sociological Research, European Society for Mathematical and Theoretical Biology, Eurostat, Institute of Mathematical Statistics, International Association for Statistics Education, International Association of Survey Statisticians, International Biometric Society, International Chinese Statistical Association, International Federation of Classification Societies, Inter- national Federation of Nonlinear Analysts, International Indian Statistical Association, International Society for Bayesian xvi Preface

Analysis, International Society for the Study of Work and Organizational Values, International Society on Multiple Crite- ria Decision Making, International Sociological Association, International Statistical Institute, Islamic Countries Society of Statistical Sciences, Omega Rho, Psychometric Society, Scandinavian Demographic Society, Sensometrics Society, Society for Applied Multivariate Research, Society for Marketing Advances, Statistical Modelling Society,andUnited Nations Statistical Commission; The major help throughout the realization of this project I received is from the following Organizational Committee members: Professor Jasmin Komic´,ProfessorKsenija Dumiciˇ c´ and Professor Milan Merkle. It is fair to say that the whole idea of Lexicon came out in my long stimulating discussions with Dr. Komic,´ after we published our joint statis- tics textbook for the university students in Republic of Srpska. Also, I would like to mention my close friend, Professor Vladislav Miloševic´ who was not fortunate enough to see this book as he passed away in . He was always there to encouragemeandtosharetheideas. I am extremely grateful to all of our reviewers whose constructive comments greatly improved many entries. In this project peer-to-peer reviewing process was applied, and many of our contributors took a dual role and reviewed papers from their field of expertise. Their valuable help is here acknowledged with gratitude. In the reviewing process, however, many papers had to be rejected, since the highest possible standard was applied. Additionally, I am sorry to say that for many papers I could not find the scholars that had time and willingness to provide me a report on these papers. Asa result we have about  papers still waiting for the referees, and hopefully some will be published in the next edition. Very special thanks are offered to the following (external) reviewers:

Alexei Stepanov – Professor, Kaliningrad State Technical University, Russia B.L.S. Prakasa Rao – Professor, University of Hyderabad, India Catherine Donati-Martin – Researcher, Université Paris VI, France Christian Genest – Professor, McGill University, Canada Damaraju Raghavarao – Professor, Temple University, USA David A. Kenny – Professor, University of Connecticut, USA Edward Waymire – Professor, Oregon State University, USA Fernando A. Quintana – Professor, Pontificia Universidad Católica de Chile, Chile Hassan Sedaghat – Professor, Virginia Commonwealth University, USA Joakim Nivre, Professor, Växjö University, Sweden Karan P. Singh – Professor, University of North Texas Health Science Center, USA Klaus Dietz – Professor Emeritus, Eberhard-Karls-University of Tübingen, Germany Laurens de Haan – Professor, Erasmus University Rotterdam, The Netherlands Linda J. S. Allen – Professor, Texas Tech University, USA Martin Bohner – Professor, Missouri University of Science and Technology, USA Philip Protter – Professor, Cornell University, USA Richard Groeneveld – Professor Emeritus, Iowa State University, USA Rinaldo Schinazi – Professor, University of Colorado, USA Sandy M. Davie, Professor, The University of Edinburgh, UK Saralees Nadarajah – Senior Lecturer, University of Manchester, UK Sergios Theodoridis – Professor, University of Athens, Greece Theresa Kline – Professor, University of Calgary, Canada Tim Bollerslev – Professor, Duke University Vladimir I. Piterbarg – Professor, Moscow Lomonosov State University, Russia William G. Faris – Professor, University of Arizona, USA

In particular, I am indebted to the Dean of my faculty, Professor Slobodan Malinic´ for his great support, especially for giving me a special permission to work continuously during the nights (till  am) at my faculty office for more than a year. Thanks are also due to my teaching assistants Marina Milanovic´ and Milan Stamenkovic´ for the long hours they spent during the corrections of the papers converted to LaTeX. The draft conversion was done by the postgraduate student Srdjan Radovanovic,´ he did a marvelous job by converting several hundred mainly difficult papers into LaTeX. Preface xvii

Thanks are also due to Springer’s editors Dr. Niels Peter Thomas and Jennifer A. Carlson for many invaluable sugges- tions, support, organization, efficiency, and kindness throughout the entire project. This encyclopedia would hardly have been possible without their participation. It would be highly inappropriate to single out any of the contributed authors. I would only like to mention that the first paper was written by Professor Peter Hall and the last one by Professor C.R Rao. There were many ups and downs, and also many critical moments during the realization of this huge project. I succeeded (better to say survived) owing to two factors. ) I was very fortunate to have had never-ending support of my wife and family. ) Whenever there was a crisis or some extremely difficult phase (like for example building cross-references, there are about  “external” and few thousand inline ones), I received an unprecedented support and encouragements from our authors that gave me the additional energy and strength to carry on.

September  Miodrag Lovric Editor-in-Chief Department of Statistics and Informatics Faculty of Economics, University of Kragujevac City of Kragujevac Serbia

Pro Statistica Scientia, Pace et Fraternitate Gentium

About the Editor

Dr. Miodrag Lovric is Professor of Statistics, Department of Statistics and Informatics, Faculty of Economics, Univer- sity of Kragujevac, City of Kragujevac, Serbia. He obtained his Ph.D. in Statistics at the University of Belgrade in , where he worked on the efficiency and robustness of nonparametric rank tests (especially on the relevance of the Pitman asymptotic relative efficiency in the case of moderate sample size). He was teaching and performing research in Belgrade. During the war in Yugoslavia, he decided to leave Serbia and move to New Zealand. He joined the Open Polytechnic of New Zealand in  and was involved in distance education. In  he joined Wellington Polytechnic (now part of the Massey University), where he delivered a range of courses starting from programming languages, data analysis, and quality assurance to applied statistics. In , he moved to Australia to join the School of Mathematics and Statistics at the University of South Australia, Adelaide. He was responsible for teaching statistics to a broad spectrum of students in the fields of business, engineering, pharmacy, biology, chemistry, and science. During this period he received from many students very negative comments about the usefulness of statistics and realized that something radically new has to be done to convey the relevance, beauty, and the universal value of statistical thinking and reasoning to them. He thought that some new educational, user-friendly, statistical software that would guide users and help choose the optimal method and provide interpretations of the results could create a friendlier attitude toward statistics. Therefore, he spent several years designing and developing such statistical software (titled EduStat). In , he moved back to Serbia and was appointed as a Professor of Statistics at the University of Belgrade and at the University of Kragujevac since . Although his statistical software is currently in use at more than  faculties in this region and presented in many TV channels in Serbia, Dr. Lovric was unable to make any significant impact and attract new students for statistics in Serbia. Soon he realized that statistics education is in deep crisis in almost all of the former Yugoslavian republics, and from  has completely devoted himself to a new project that finally resulted in this Encyclopedia. Dr. Lovric has (co)authored many papers and several statistics textbooks (mainly in Serbian) that are widely used in this region. Recently, he had delivered lectures for undergraduate, graduate, postgraduate, and Ph.D. students in Eco- nomics, Pharmaceutical Medicine, and Veterinary Science in Serbia and Bosnia. He was a leader of many projects, including the ones for the Belgrade Stock Exchange, Ministry of Trade and Tourism, Ministry of Finance, and Min- istry of Internal Affairs, Serbia. He has designed and developed several software products for the company Insight Data in Auckland, New Zealand, and an election software for one of the leading parties in New Zealand. He is a member of the xx About the Editor

Editorial board of the Statistics Review, the only statistics journal in this region. Recently, he has been elected as a member of the panel of examiners for Ph.D. students in several countries. In , he was elected as President of the International Federation of Nonlinear Analysts (Serbian Branch). His research interests are very broad, including philosophy and foun- dations of statistical science, statistics education, history of statistics and statistical software. He has also a keen interest in the evolution, creationism, and intelligent design controversy, special and general theory of relativity (including their criticism), theory of parallel universes, and cosmology. However, with the realization that in more than  countries in the world there is not a single professor in statistics, his main focus became a quest to find ways to revive statistics education in this region as well as in many developing countries. Professor Lovric is a Fellow of the Royal Statistical Society. List of Contributors

Khidir M. Abdelbasit S. Ejaz Ahmed Sultan Qaboos University University of Windsor Muscat Windsor, ON Sultanate of Oman Canada

Mohamed Abdel-Hameed Mohammad Ahsanullah United Arab Emirates University Rider University Al Ain Lawrenceville, NJ United Arab Emirates USA

Abdurahim Abdushukurov Hirotugu Akaike† National University of Uzbekistan Tokyo Tashkent Japan Uzbekistan

Juan Carlos Abril Michael G. Akritas Universidad Nacional de Tucumán and Consejo Pennsylvania State University Nacional de Investigaciones Científicas y Técnicas State College, PA San Miguel de Tucumán USA Argentina

Asghar Ali Edgar Acuña Bahauddin Zakariya University University of Puerto Rico at Mayaguez Multan Mayaguez Pakistan Puerto Rico

Gerold Alsmeyer John Adams Institut für Mathematische Statistik Baylor Health Care System Münster Dallas, TX Germany USA

Mohammed I. Ageel Isabel Fraga Alves Jazan University University of Lisbon Jazan Lisbon Saudi Arabia Portugal

Alan Agresti Emad-Eldin A. A. Aly University of Florida Kuwait University Gainesville, FL Safat USA Kuwait xxii List of Contributors

Margo J. Anderson Lynda Atil University of Wisconsin–Milwaukee University of Tizi-Ouzou Milwaukee, WI Tizi-Ouzou USA Algeria

Per Kragh Andersen University of Copenhagen Anthony C. Atkinson Copenhagen London School of Economics Denmark London UK

Theodore W. Anderson Stanford University Stanford, CA Thomas Augustin USA Ludwig Maximilian University Munich Germany Paola Annoni Institute for the Protection and the Security of the Citizen Ispra Adnan M. Awad Italy University of Jordan Amman Jordan Demetrios L. Antzoulakos University of Piraeus Piraeus Greece H. Özta¸sAyhan Middle East Technical University Ankara David Applebaum Turkey University of Sheffield Sheffield UK Adelchi Azzalini University of Padua J. Scott Armstrong Padua University of Pennsylvania Italy Philadelphia, PA USA

Barry J. Babin Kenneth J. Arrow Louisiana Tech University Stanford University Ruston, LA San Jose, CA USA USA

Hossein Arsham Vlasta Bahovec University of Baltimore University of Zagreb Baltimore, MD Zagreb USA Croatia List of Contributors xxiii

Zhidong Bai Bojan Basrak Northeast Normal University University of Zagreb Changchun Zagreb China Croatia

Charles R. Baker University of North Carolina Mojca Bavdaž Chapel Hill, NC University of Ljubljana USA Ljubljana Slovenia

Badi H. Baltagi Abdulbari Bener Syracuse University Weill Cornell Medical College Syracuse, NY Doha USA Qatar

Ravindra B. Bapat Jan Beran Indian Statistical Institute University of Konstanz New Delhi Konstanz India Germany

Anna E. Bargagliotti Rudolf Beran University of Memphis University of California-Davis Memphis, TN Davis, CA USA USA

Erniel B. Barrios Mark L. Berenson University of the Philippines Montclair State University Quezon City Montclair, NJ Philippines USA

David J. Bartholomew José M. Bernardo London School of Economics and Political Science Universitat de València London Burjassot UK Spain

Ishwar V. Basawa Nejc Berzelak University of Georgia University of Ljubljana Athens, GA Ljubljana USA Slovenia

Bojana Dalbelo Bašic´ Jelke Bethlehem University of Zagreb University of Amsterdam Zagreb Amsterdam Croatia Netherlands xxiv List of Contributors

U. Narayan Bhat Graciela Boente Southern Methodist University Universidad de Buenos Aires and CONICET Dallas, TX Buenos Aires USA Argentina

Rabi Bhattacharya John Boland The University of Arizona University of South Australia Tucson, AZ Adelaide, SA USA Australia

Paul P.Biemer Lennart Bondesson RTI International and the University of North Carolina Umeå University Chapel Hill, NC Umeå USA Sweden

Silvia Biffignandi Bergamo University David L. Borchers Bergamo University of St Andrews Italy St Andrews UK

Maja Biljan-August University of Rijeka Ingwer Borg Rijeka University of Giessen Croatia Giessen Germany and Wolfgang Bischoff GESIS Catholic University Eichstätt–Ingolstadt Mannheim Eichstätt Germany Germany

Alexander Alekseevich Borovkov Kalina Trenevska Blagoeva Novosibirsk University University “Ss. Cyril and Methodius” Novosibirsk Skopje Russia Macedonia

Jörg Blasius Adrian W. Bowman University of Bonn The University of Glasgow Bonn Glasgow Germany UK

Hans-Peter Blossfeld Kimiko O. Bowman Otto-Friedrich-Universität Bamberg Oak Ridge National Laboratory Bamberg Oak Ridge, TN Germany USA List of Contributors xxv

G. E. P.Box Enrique M. Cabaña University of Wisconsin Universidad de la República Madison, WI Monterideo USA Uruguay

F. Jay Breidt Colorado State University Ricardo Cao Fort Collins, CO Universidade da Coruña USA ACoruña Spain

Per Bruun Brockhoff Technical University of Denmark Lyngby Vincenzo Capasso Denmark University of Milan Milan Italy Peter J. Brockwell Colorado State University Fort Collins, CO Vincent J. Carey USA Brigham and Women’s Hospital Boston, MA Jennifer Brown USA University of Canterbury Christchurch New Zealand MarcoE.G.V.Cattaneo Ludwig Maximilian University Munich Vesna Bucevska Germany University “Ss. Cyril and Methodious” Skopje Macedonia Joseph E. Cavanaugh The University of Iowa Stephen T. Buckland Iowa City, IA University of St Andrews USA St Andrews UK

Subhabrata Chakraborti Murray D. Burke The University of Alabama University of Calgary Tuscaloosa, AL Calgary, AB USA Canada

Vesna Buško Tapas Kumar Chandra University of Zagreb Indian Statistical Institute Zagreb Calcutta Croatia India xxvi List of Contributors

Samprit Chatterjee Christy Chuang-Stein Graduate School of Business Administration Pfizer Inc. New York, NY Kalamazoo, MI USA USA and New York University New York, NY USA Yuk Ka Chung University of Hong Kong Hong Kong China Michael R. Chernick Lankenau Institute for Medical Research Wynnewood, PA USA Mirjana Cižmešijaˇ University of Zagreb Zagreb Herman Chernoff Croatia Harvard University Cambridge, MA USA Gerda Claeskens K.U. Leuven Devendra Chhetry Leuven Tribhuvan University Belgium Kathmandu Nepal Stephen R. Clarke Swinburne University Siddhartha Chib Melbourne, VIC Washington University in St. Louis Australia St. Louis, MO USA

James J. Cochran Hugh A. Chipman Louisiana Tech University Acadia University Ruston, LA Wolfville, NS USA Canada

Allan S. Cohen John S. Chipman University of Georgia University of Minnesota Athens, GA Minneapolis, MN USA USA

S. Chitsaz Arthur Cohen University of Windsor Rutgers University Windsor, ON Piscataway, NJ Canada USA List of Contributors xxvii

Michael P.Cohen Francisco José A. Cysneiros NORC at the University of Chicago CCEN-UFPE - Cidade Universitária - Recife Chicago, IL Recife USA Brazil and George Mason University Fairfax, VA Takashi Daimon USA Hyogo College of Medicine Hyogo Japan Francis Comets and Université Paris Diderot Osaka University Hospital Paris Osaka France Japan

W. J. Conover Jacques Dauxois Texas Tech University Institut de Mathématiques de Toulouse Lubbock, TX Toulouse USA France

R. Dennis Cook Herbert A. David University of Minnesota Iowa State University Minneapolis, MN Ames, IA USA USA

Marie Davidian FrankP.A.Coolen North Carolina State University Durham University Raleigh, NC Durham USA UK

Anthony C. Davison Gauss M. Cordeiro Ecole Polytechnique Fédérale de Lausanne, Universidade Federal Rural de Pernambuco EPFL-FSB-IMA-STAT Recife Lausanne Brazil Switzerland

D. R. Cox Herold Dehling Nuffield College Ruhr-Universität Bochum Oxford Bochum UK Germany

Rosa M. Crujeiras Mohan Delampady University of Santiago de Compostela Indian Statistical Institute Santiago de Compostela Bangalore Spain India xxviii List of Contributors

David A. Dickey Luc Duchateau North Carolina State University Ghent University Raleigh, NC Ghent USA Belgium

Ksenija Dumicic Peter J. Diggle University of Zagreb Lancaster University Zagreb Lancaster Croatia UK and Johns Hopkins University School of Public Health Graham Dunn Baltimore, MD University of Manchester USA Manchester and UK Columbia University New York, NY USA Rick L. Edgeman University of Idaho Moscow, ID Herman K. van Dijk USA Erasmus University Rotterdam Rotterdam Eugene S. Edgington The Netherlands University of Calgary Calgary, AB Canada Dražen Domijan University of Rijeka Rijeka David J. Edwards Croatia Virginia Commonwealth University Richmond, VA USA

Atsu S. S. Dorvlo Sultan Qaboos University Bradley Efron Muscat Stanford University Sultanate of Oman Stanford, CA USA

David Draper University of California-Santa Cruz Joseph G. Eisenhauer Santa Cruz, CA University of Detroit Mercy USA Detroit, MI USA

Steve Drekic Mhamed-Ali El-Aroui University of Waterloo ISG de Tunis Waterloo, ON Bardo Canada Tunisia List of Contributors xxix

Mohamed Y. El-Bassiouni S. Fallahpour United Arab Emirates University University of Windsor Al-Ain Windsor, ON United Arab Emirates Canada

Abdalla M. El-Habil Al-Azhar University Kai-Tai Fang Gaza Beijing Normal University-Hong Kong Baptist University Palestine Zhuhai China

Saïd El Melhaoui Université Mohammed Premier Richard William Farebrother Oujda Victoria University of Manchester Morocco Manchester UK Paul Embrechts ETH Zurich Zurich Daniel M. Farewell Switzerland School of Medicine Cardiff University Cardiff Nataša Erjavec UK University of Zagreb Zagreb Croatia Vern T. Farewell Medical Research Council Elena A. Erosheva Biostatistics Unit University of Washington Cambridge Seattle, WA UK USA

Pedro J. Rodríguez Esquerdo Eric D. Feigelson University of Puerto Rico Pennsylvania State University San Juan University Park, PA Puerto Rico USA

B. S. Everitt Hocine Fellag Institute of Psychiatry University of Tizi-Ouzou King’s College Tizi-Ouzou London Algeria UK

Ludwig Fahrmeir Johan Fellman Ludwig-Maximilians-University Folkhälsan Institute of Genetics Munich Helsinki Germany Finland xxx List of Contributors

Anuška Ferligoj Konstantinos Fokianos University of Ljubljana University of Cyprus Ljubljana Nicosia Slovenia Cyprus

Zoila Fernández Noël H. Fonton Universidad Católica del Norte University of Abomey-Calavi Antofagasta Cotonou Chile Benin Republic

Luisa Turrin Fernholz Ove Frank Temple University Stockholm University Philadelphia, PA Stockholm USA Sweden

Cristiano Ferraz Federal University of Pernambuco D. A. S. Fraser Recife University of Toronto Brazil Toronto, ON Canada

Linda S. Fidell California State University Barbara M. Fraumeni Northridge, CA University of Southern Maine USA Portland, ME USA

Stephen E. Fienberg Carnegie Mellon University Roland Fried Pittsburgh, PA TU Dortmund University USA Dortmund Germany Giovanni Filardo Baylor Health Care System Dallas, TX Arnoldo Frigessi USA Norwegian Centre for Research-Based Innovation Oslo Norway Matthias Fischer and University of Erlangen-Nürnberg University of Oslo & Norwegian Computing Centre Erlangen Oslo Germany Norway

David Fletcher Marianne Frisén University of Otago University of Gothenburg Dunedin Gothenburg New Zealand Sweden List of Contributors xxxi

Wing Kam Fung James E. Gentle University of Hong Kong George Mason University Hong Kong Fairfax, VA China USA

Mirta Galesic Robert Gentleman Max Planck Institute for Human Development Genentech Berlin South San Francisco, CA Germany USA

Joan Garfield Ann Cathrice George University of Minnesota TU Dortmund University Minneapolis, MN Dortmund USA Germany

G. David Garson Jayanta K. Ghosh North Carolina State University Purdue University Raleigh, NC West Lafayette, IN USA USA

Paul H. Garthwaite Sucharita Ghosh The Open University Swiss Federal Research Institute WSL Milton Keynes Birmensdorf UK Switzerland

Joseph L. Gastwirth Jean Dickinson Gibbons George Washington University The University of Alabama Washington, DC Tuscaloosa, AL USA USA

Ursula Gather Irène Gijbels TU Dortmund University Katholieke Universiteit Leuven Dortmund Leuven Germany Belgium

Sara van de Geer Richard D. Gill ETH Zürich Leiden University Zürich Leiden Switzerland Netherlands

Zhi Geng Evarist Giné Peking University University of Connecticut Beijing Storrs, CT China USA xxxii List of Contributors

Harvey Goldstein Sander Greenland University of Bristol University of California-Los Angeles Bristol Los Angeles, CA UK USA

M. Ivette Gomes Mohinder S. Grewal Universidade de Lisboa California State University DEIO and CEAUL, Lisboa Fullerton, CA Portugal USA

Wenceslao González-Manteiga Bronius Grigelionis University of Santiago de Compostela Institute of Mathematics and Informatics Santiago de Compostela Vilnius Spain Lithuania

Leticia Gracia-Medrano Robert J. Grissom IIMAS San Francisco State University UNAM, México City San Francisco, CA México USA

Andreas Graefe Lelys Bravo de Guenni Karlsruhe Institute of Technology Universidad Simón Bolívar Karlsruhe Caracas Germany Venezuela

Clive William John Granger† Frank M. Guess University of California-San Diego University of Tennessee San Diego, CA Knoxville, TN USA USA

Mary W. Gray Renkuan Guo American University University of Cape Town Washington DC Cape Town USA South Africa

Kesten C. Green Arjun K. Gupta University of South Australia Bowling Green State University Adelaide, SA Bowling Green, OH Australia USA

Michael R. Greenberg S. N. Gupta Rutgers University University of South Pacific New Brunswick, NJ Suva USA Fiji List of Contributors xxxiii

Peter Hackl Nor Aishah Hamzah Vienna University of Business and Economics University of Malaya Vienna Kuala Lumpur Austria Malaysia

Ali S. Hadi The American University in Cairo David Hand Cairo Imperial College Egypt London and UK Cornell University Ithaca, NY USA Jan Hannig The University of North Carolina at Chapel Hill Olga Hadžic´ Chapel Hill, NC University of Novi Sad USA Novi Sad Serbia Sven Ove Hansson Royal Institute of Technology Joseph F. Hair Stockholm Kennesaw State University Sweden Kennesaw, GA USA

Evgueni Haroutunian Asaf Hajiyev Institute for Informatics and Automation Problems of Baku State University the Armenian National Academy of Sciences Baku Yerevan Azerbaijan Armenia

Peter Hall The University of Melbourne Dieter Hauschke Australia University Medical Centre Freiburg and Freiburg University of California Germany Davis, CA USA

John Haywood Toshimitsu Hamasaki Victoria University of Wellington Osaka University Graduate School of Medicine Wellington Osaka New Zealand Japan

James D. Hamilton Martin L. Hazelton University of California Massey University San Diego, CA Palmerston North USA New Zealand xxxiv List of Contributors

Xin He Joseph M. Hilbe University of Maryland University of Hawaii College Park, MD Honolulu, HI USA USA and Arizona State University James J. Heckman Tempe, AZ The University of Chicago USA Chicago, IL and USA California Institute of Technology and Pasadena, CA University College Dublin USA Dublin Ireland John Hinde National University of Ireland Galway Bernd Heidergott Ireland Vrije Universiteit Amsterdam The Netherlands Klaus Hinkelmann Virginia Polytechnic Institute and State University Blacksburg, VA Inge S. Helland USA University of Oslo Oslo Paul von Hippel Norway University of Texas Austin, TX USA Carlos N. Bouza Herrera Universidad de La Habana Habana Nikica Hlupic´ Cuba University of Zagreb Zagreb Croatia Scott L. Hershberger Harris Intractive Jan M. Hoem New York, NY Max Planck Institute for Demographic Research USA Rostock Germany

Thomas P.Hettmansperger Penn State University Alexander S. Holevo State College, PA Steklov Mathematical Institute USA Moscow Russia

Christian Heumann D. S. Hooda Ludwig Maximilian University Jaypee University of Engineering and Technology Munich Guna Germany India List of Contributors xxxv

Lennart Hoogerheide Peter J. Huber Erasmus University Rotterdam Klosters Rotterdam Switzerland The Netherlands

Wolfgang Huber Jasna Horvat Heidelberg J.J. Strossmayer University Germany Osijek Croatia Mia Hubert Katholieke Universiteit Leuven Shakhawat Hossain Leuven University of Windsor Belgium Windsor, ON Canada

Carl J. Huberty Norbert Hounkonnou University of Georgia University of Abomey-Calavi Athens, GA Cotonou USA Benin Republic

Shahariar Huda David C. Howell Kuwait University University of Vermont Safat Burlington, VT Kuwait USA

Miljenko Huzak Florentina T. Hristea University of Zagreb University of Bucharest Zagreb Bucharest Croatia Romania

Svend Hylleberg Francis Hsuan University of Aarhus Temple University Aarhus C Philadelphia, PA Denmark USA

Deng-Yuan Huang Rob J. Hyndman Fu-Jen Catholic University Monash University Taipei Melbourne, VIC Taiwan Australia

Raymond Hubbard Marat Ibragimov Drake University Tashkent State University of Economics Des Moines, IA Tashkent USA Uzbekistan xxxvi List of Contributors

Rustam Ibragimov Donald R. Jensen Harvard University Virginia Polytechnic Institute and State University Cambridge, MA Blacksburg, VA USA USA

Boris Iglewicz Daniel R. Jeske Temple University University of California-Riverside Philadelphia, PA Riverside, CA USA USA

Ronald L. Iman Vesna Jevremovic´ Southwest Technology Consultants University of Belgrade Albuquerque, NM Belgrade USA Serbia

Gudmund R. Iversen Anwar H. Joarder Swarthmore College King Fahd University of Petroleum and Minerals Swarthmore, PA Dhahran USA Saudi Arabia

Hari Iyer Mark E. Johnson Colorado State University University of Central Florida Fort Collins, CO Orlando, FL USA USA

Alan J. Izenman Richard A. Johnson Temple University University of Wisconsin Philadelphia, PA Madison, WI USA USA

Maarten Jansen William D. Johnson Universite´ libre de Bruxelles Louisiana State University Brussels Baton Rouge, LA Belgium USA

Paul Janssen Ian Jolliffe Hasselt University University of Exeter Diepenbeek Exeter Belgium UK

Carlos M. Jarque David S. Jones Inter American Development Bank Queens University of Belfast Paris Belfast France UK List of Contributors xxxvii

Bent Jørgensen Adrienne W. Kemp University of Southern Denmark University of St. Andrews Odense M St. Andrews Denmark UK

James M. Joyce University of Michigan Peter Kennedy Ann Arbor, MI Simon Fraser University USA Burnaby, BC Canada

Jana JureckovᡠCharles University in Prague Prague Eamonn J. Keogh Czech Republic University of California-Riverside Riverside, CA USA Joseph B. Kadane Carnegie Mellon University Pittsburg, PA Jon R. Kettenring USA Drew University Madison, NJ Damir Kalpic´ USA University of Zagreb Zagreb Croatia Sekander Hayat Khan M. Institute of Statistical Research and Training University of Dhaka Graham Kalton Dhaka Westat Bangladesh Rockville, MD USA

Yuriy S. Kharin Maria Kateri Belarus State University University of Ioannina Minsk Ionnina Belarus Greece

Hannes Kazianka Estate V. Khmaladze University of Technology Victoria University of Wellington Vienna Wellington Austria New Zealand

Cónall Kelly University of the West Indies André I. Khuri Mona Campus University of Florida Kingston Gainesville, FL Jamaica USA xxxviii List of Contributors

Anwer Khurshid Fejzi Kolaneci University of Karachi University of New York Karachi Tirana Pakistan Albania

Rüdiger Kiesel John E. Kolassa Universität Duisburg-Essen Rutgers University Duisburg Newark, NJ Germany USA

Alexander D. Kolesnik Seock-Ho Kim Institute of Mathematics & Computer Science University of Georgia Academy of Sciences of Moldova Athens, GA Kishinev USA Moldova

Roger E. Kirk Jasmin Komic´ Baylor University University of Banja Luka Waco, TX Republic of Srpska USA Bosnia and Herzegovina

Takis Konstantopoulos Christos P.Kitsos Heriot-Watt University Technological Educational Institute of Athens Edinburgh Athens UK Greece

Hira L. Koul Peter E. Kloeden Michigan State University Goethe-Universität East Lansing, MI Frankfurt USA Germany

Walter Krämer Jan Kmenta Technische Universität Dortmund University of Michigan Dortmund Ann Arbor, MI Germany USA and Kalimuthu Krishnamoorthy Center for Economic Research and Graduate Education University of Louisiana at Lafayette Prague Lafayette, LA Czech Republic USA

Gary G. Koch Venkatarama Krishnan University of North Carolina UMass Lowell Chapel Hill, NC Lowell, MA USA USA List of Contributors xxxix

Zarylbek I. Kudabaev Anil G. Ladde American University of Central Asia Chesapeake Capital Corporation Bishkek Richmond, VA Kyrgyz Republic USA

Sonja Kuhnt Gangaram S. Ladde TU Dortmund University University of South Florida Dortmund Tampa, FL Germany USA

Alexander Kukush Chin Diew Lai National Taras Shevchenko University of Kyiv Massey University Kyiv Palmerston North Ukraine New Zealand

Elena Kulinskaya Steven P.Lalley University of East Anglia University of Chicago Norwich Chicago, IL UK USA

Pranesh Kumar David Lane University of Northern British Columbia Rice University Prince George, BC Houston, TX Canada USA

Debasis Kundu M. R. Leadbetter Indian Institute of Technology Kanpur University of North Carolina Kanpur Chapel Hill, NC India USA

Robert M. Kunst Bruno Lecoutre University of Vienna C.N.R.S. and Université de Rouen Vienna Mont Saint Aignan Austria France

Parinbanu Kurji Pierre L’Ecuyer University of Nairobi Université de Montréal Nairobi Montréal, QC Kenya Canada

Tarald O. Kvålseth Herbert K. H. Lee University of Minnesota University of California-Santa Cruz Minneapolis, MN Santa Cruz, CA USA USA xl List of Contributors

Jaeyong Lee Pui Lam Leung Seoul National University The Chinese University of Hong Kong Seoul Hong Kong Korea China

Mei-Ling Ting Lee David M. Levine University of Maryland Baruch College College Park, MD City University of New York USA New York, NY USA

Thomas C. M. Lee The University of California at Davis Toby Lewis Davis, CA University of East Anglia USA Norwich UK

Lawrence M. Leemis The College of William & Mary Roderick J. Little Williamsburg, VA University of Michigan USA Ann Arbor, MI USA Jan de Leeuw University of California-Los Angeles Lefei Liu Los Angeles, CA University of South Carolina USA Columbia, SC USA Erich Leo Lehmann† University of California Berkeley, CA Shuangzhe Liu USA University of Canberra Canberra, ACT Australia Subhash R. Lele University of Alberta Edmonton, AB Nicholas T. Longford Canada Universitat Pompeu Fabra Barcelona Spain Raoul LePage Michigan State University East Lansing, MI Raul H. C. Lopes USA Brunel University Uxbridge UK James M. Lepkowski and University of Michigan UFES Ann Arbor, MI Vitoria USA Brazil List of Contributors xli

Thomas A. Louis Tapabrata Maiti Johns Hopkins Bloomberg School of Public Health Michigan State University Baltimore, MD East Lansing, MI USA USA

Francisco Louzada-Neto Aboubakar Maitournam Universidade Federal de São Carlos University Abdou Moumouni of Niamey Sao Paulo Niamey Brazil Niger

Miodrag Lovric´ Janez Malaciˇ cˇ University of Kragujevac University of Ljubljana Kragujevac Ljubljana Serbia Slovenia

Colin Mallows Alberto Luceño Basking Ridge University of Cantabria Avayalabs, NJ Santander USA Spain

Saumen Mandal Helmut Lütkepohl University of Manitoba European University Institute Winnipeg, MB Firenze Canada Italy

Katja Lozar Manfreda Peter Lynn University of Ljubljana University of Essex Ljubljana Colchester Slovenia UK

Roberto S. Mariano Mohamed T. Madi Singapore Management University UAE University Singapore Al Ain Singapore United Arab Emirates

Harry M. Markowitz Yoshihiko Maesono University of California Kyushu University San Diego, CA Fukuoka USA Japan

Ricardo Maronna Smail Mahdi University of La Plata and C.I.C.P.B.A. University of The West Indies La Plata Cave Hill Campus Buenos Aires Barbados Argentina xlii List of Contributors

Tiago A. Marques Milan Merkle University of St Andrews University of Belgrade St Andrews Belgrade UK Serbia and Universidade de Lisboa Lisboa Petar Milin Portugal University of Novi Sad Novi Sad Serbia Shigeru Mase Tokyo Institute of Technology Tokyo Leda D. Minkova Japan Sofia University “St. Kl. Ohridski” Sofia Bulgaria Robert L. Mason Southwest Research Institute KostoV.Mitov San Antonio, TX National Military University USA Pleven, D. Mitropolia Bulgaria

Florance Matarise University of Zimbabwe Reza Modarres Harere The George Washington University Zimbabwe Washington, DC USA

Peter McCullagh University of Chicago Mikhail P.Moklyachuk Chicago, IL Kyiv National Taras Shevchenko University USA Kyiv Ukraine

Dante Covarrubias Melgar Geert Molenberghs Universidad Autónoma de Guerrero Universiteit Hasselt and Katholieke Universiteit Leuven Mexico City Leuven Mexico Belgium

Edward L. Melnick Jill M. Montaquila New York University Westat New York, NY Rockville, MD USA USA

Xiao-Li Meng David S. Moore Harvard University Purdue University Cambridge, MA West Lafayette, IN USA USA List of Contributors xliii

Stephan Morgenthaler Janet Myhre Ecole Polytechnique Fédérale de Lausanne Claremont McKenna College Lausanne Claremont, CA Switzerland USA

Peter Naeve Toshihiko Morikawa University of Bielefeld Kurume University Bielefeld Kurume Germany Japan

K. R. Muraleedharan Nair Thomas Mühlenstädt Cochin University of Science and Technology TU Dortmund University Cochin Dortmund India Germany

Krishnan Namboodiri Nitis Mukhopadhyay Ohio State University University of Connecticut-Storrs Columbus, OH Storrs, CT USA USA

Efendi N. Nasibov Dokuz Eylul University Hans-Georg Müller Imzir University of California-Davis Turkey Davis, CA USA Mohammed Nasser University of Rajshahi Kevin R. Murphy Rajshahi Pennsylvania State University Bangladesh University Park, PA USA Gad Nathan Hebrew University of Jerusalem Jerusalem Michael P.Murray Israel Bates College Lewiston, ME USA Andrew A. Neath Southern Illinois University Edwardsville Edwardsville, IL Fionn Murtagh USA Wilton Place, Dublin Ireland and Konstantin N. Nechval University of London Transport and Telecommunication Institute London Riga UK Latvia xliv List of Contributors

Nicholas A. Nechval Georges Nguefack-Tsague University of Latvia University of Yaoundé I Riga Yaoundé Latvia Cameroon

Abdelhakim Necir Nam-Ky Nguyen Mohamed Khider University of Biskra Vietnam National University Biskra Hanoi Algeria Vietnam

John Nelder† Raymond S. Nickerson Imperial College Tufts University London Medford, MA UK USA

Markus Neuhäuser Yakov Nikitin Koblenz University of Applied Sciences St. Petersburg University Remagen St. Petersburg Germany Russia

Cláudia Neves Mikhail Nikulin University of Aveiro Université Victor Segalen Aveiro Bordeaux Portugal France

Valery B. Nevzorov Xianghui Ning St. Petersburg State University Hong Kong University of Science and Technology St. Petersburg Hong Kong Russia China

Choung Min Ng Guy Martial Nkiet University of Malaya Université des Sciences et Techniques de Masuku Kuala Lumpur Franceville Malaysia Gabon

Hon Keung Tony Ng S. Nkurunziza Southern Methodist University University of Windsor Dallas, TX Windsor, ON USA Canada

Kai Wang Ng Kaku Sagary Nokoe The University of Hong Kong University for Development Studies Hong Kong Navrongo China Ghana List of Contributors xlv

John M. Norman William J. Padgett Sheffield University University of South Carolina Sheffield Columbia, SC UK USA

William Notz S. Panchapakesan The Ohio State University Southern Illinois University Columbus, OH Carbondale, IL USA USA

JamesP.M.Ntozi Sung H. Park Makerere University Seoul National University Kampala Seoul Uganda Korea

Justice I. Odiase Kalev Pärna University of Benin University of Tartu Benin City Tartu Nigeria Estonia

Sunday M. Ogbonmwan Andrej Pázman University of Benin Comenius University Benin City Bratislava Nigeria Slovakia

Henrik Olsson Judea Pearl Max Planck Institute for Human Development University of California-Los Angeles Berlin Los Angeles, CA Germany USA

Seng Huat Ong BasiliodeBragançaPereira University of Malaya Universidade Federal do Rio de Janeiro Kuala Lumpur Rio de Janeiro Malaysia Brazil

Jean D. Opsomer Carlos Alberto de Bragança Pereira Colorado State University Universidade de São Paulo Fort Collins, CO São Paulo USA Brazil

Federico J. O’Reilly Luis Raúl Pericchi IIMAS University of Puerto Rico UNAM, México City San Juan México Puerto Rico xlvi List of Contributors

Dinis Pestana Joaquim F. Pinto da Costa Universidade de Lisboa University of Porto Centro de Estatística e Aplicações da Universidade de Porto Lisboa Portugal Lisboa Portugal Biljana C.ˇ Popovic´ University of Niš Martin Peterson Niš Eindhoven University of Technology Serbia Eindhoven Netherlands Zoran R. Pop-Stojanovic´ University of Florida Sonja Petrovic´ Gainesville, FL University of Illinois at Chicago USA Chicago, IL USA Petra Posedel University of Zagreb Danny Pfeffermann Zagreb Hebrew University of Jerusalem Croatia Jerusalem Israel and Tiberiu Postelnicu University of Southampton Romanian Academy Southampton Bucharest UK Romania

Andreas N. Philippou Samir Pradhan University of Patras Economics Program at the Gulf Research Center Patras Dubai Greece United Arab Emirates

Walter W. Piegorsch Tommaso Proietti University of Arizona University of Rome “Tor Vergata” Tucson, AZ Rome USA Italy

Jürgen Pilz Llukan Puka University of Klagenfurt University of Tirana Klagenfurt Tirana Austria Albania

Aluísio de Souza Pinheiro Simo Puntanen University of Campinas University of Tampere Campinas Tampere Brazil Finland List of Contributors xlvii

Maris Purgailis M. F. Ramalhoto University of Latvia Technical University of Lisbon Riga Lisbon Latvia Portugal

Madan Lal Puri R. V. Ramamoorthi King Fahd University of Petroleum and Minerals Michigan State University Dhahran East Lansing, MI Saudi Arabia USA and Indiana University Bloomington, IN C. R. Rao USA C. R. RAO AIMSCS Hyderabad India Peihua Qiu and University of Minnesota Pennsylvania State University Minneapolis, MN University Park, PA USA USA

J. N. K. Rao T. Quadir Carleton University University of Windsor Ottawa, ON Windsor, ON Canada Canada

Mohammad Z. Raqab Walter J. Radermacher University of Jordan Eurostat Amman Luxembourg Jordan

Enayetur Raheem Pushpa Narayan Rathie University of Windsor University of Brasilia Windsor, ON Brasilia Canada Brazil

Markku Rahiala Tenko Raykov University of Oulu Michigan State University Oulu East Lansing, MI Finland USA

M. B. Rajarshi Rolando Rebolledo University of Pune Universidad Catolica de Chile Pune Santiago India Chile xlviii List of Contributors

Thomas C. Redman Alexandra Rodkina Navesink Consulting Group University of the West Indies Rumson, NJ Mona Campus USA Kingston Jamaica

Nancy Reid University of Toronto Isabel M. Rodrigues Toronto, ON Technical University of Lisbon Canada Lisboa Portugal

Jerome P. Reiter Vijay K. Rohatgi Duke University Bowling Green State University Durham, NC Bowling Green, OH USA USA

Bruno Rémillard H. Charles Romesburg HEC Montréal Katowice University of Economics Montréal, QC Katowice Canada Poland

Eric A. Rexstad Elvezio Ronchetti University of St Andrews University of Geneva St Andrews Geneva UK Switzerland

Denise Rey Andrew Rosalsky Rey Analytical Research University of Florida Hürth Gainesville, FL Germany USA

Horst Rinne Colin Rose Justus–Liebig–University Giessen Theoretical Research Institute Giessen Sydney, NSW Germany Australia

Alfredo Rizzi Gavin J. S. Ross Sapienza Università di Rome Rothamsted Research Rome Harpenden Italy UK

Christian Robert Joseph S. Rossi Université Paris-Dauphine University of Rhode Island CEREMADE, Paris Kingston, RI France USA List of Contributors xlix

Peter J. Rousseeuw Hardeo Sahai Renaissance Technologies University of Puerto Rico New York, NY San Juan USA Puerto Rico

Jože Rovan University of Ljubljana Mohammad Salehi M. Ljubljana Isfahan University of Technology Slovenia Isfahan Iran

Patrick Royston University College London London Andrea Saltelli UK Institute for the Protection and the Security of the Citizen Ispra Boris L. Rozovski˘ı Italy Brown University Providence, RI USA Francisco J. Samaniego University of California-Davis Donald B. Rubin Davis, CA Harvard University USA Cambridge, MA USA Dimitri Sanga African Centre for Statistics Herman Rubin Addis Ababa Purdue University Ethiopia West Lafayette, IN USA

Lino Sant Tamás Rudas University of Malta Eötvös Loránd University Msida Budapest Malta Hungary

Donald G. Saari Sanat K. Sarkar University of California-Irvine Temple University Irvine, CA Philadelphia, PA USA USA

Ashok Sahai St. Augustine Campus of the University of the West Willi Sauerbrei Indies at Trinidad University Medical Center Freiburg St. Augustine Freiburg Trinidad and Tobago Germany l List of Contributors

Jack Sawilowsky Edith Seier Wayne State University East Tennessee State University Detroit, MI Johnson City, TN USA USA

Shlomo Sawilowsky Carlo Sempi Wayne State University Università del Salento Detroit, MI Lecce USA Italy

Bruno Scarpa Pranab K. Sen University of Padua University of North Carolina Padua Chapel Hill, NC Italy USA

Richard L. Scheaffer Robert Serfling University of Florida University of Texas at Dallas Gainesville, FL Richardson, TX USA USA

Michael G. Schimek Jayaram Sethuraman Medical University of Graz Florida State University Graz Tallahassee, FL Austria USA

Alastair Scott Yanfen Shang The University of Auckland Hong Kong University of Science and Technology Auckland Hong Kong New Zealand China

David W. Scott Dahud K. Shangodoyin Rice University University of Botswana Houston, TX Gaborone USA Botswana

George A. F. Seber Olimjon Shukurovich Sharipov Auckland University Uzbek Academy of Sciences Auckland Tashkent New Zealand Uzbekistan

Wilfried Seidel Simon J. Sheather Helmut-Schmidt-Universität Texas A&M University Hamburg College Station, TX Germany USA List of Contributors li

L. R. Shenton Charilaos Skiadas University of Georgia Hanover College Athens, GA Hanover, IN USA USA

David J. Sheskin Western Connecticut State University Christos H. Skiadas Danbury, CT Technical University of Crete USA Chania Greece

Oscar Sheynin Berlin Aleksandra B. Slavkovic´ Germany The Pennsylvania State University University Park, PA USA Albert N. Shiryaev Moscow State University Moscow Russia Leslie S. Smith University of Stirling Stirling Kyle Siegrist UK University of Alabama in Huntsville Huntsville, AL USA StephenL.J.Smith University of Waterloo Jack W. Silverstein Waterloo, ON North Carolina State University Canada Raleigh, NC USA Kate Smith-Miles Monash University Vassiliy Simchera Melbourne, VIC Rosstat’s Statistical Research Institute Australia Moscow Russia

Michael Smithson JulioM.Singer The Australian National University Universidade de São Paulo Canberra, ACT São Paulo Australia Brazil

Mahender Singh Robert T. Smythe Massachusetts Institute of Technology Oregon State University Cambridge, MA Corvallis, OR USA USA lii List of Contributors

TomA.B.Snijders Aris Spanos University of Oxford Virginia Tech Oxford Blacksburg, VA UK USA and University of Groningen Groningen Edward J. Spar Netherlands Council of Professional Associations on Federal Statistics Alexandria, VA USA Ger Snijkers Utrecht University Utrecht Gunter Spöck The Netherlands University of Klagenfurt and Klagenfurt Senior Researcher in Business Survey Data Collection Austria Methodology at Statistics The Netherlands Peter Sprent University of Dundee Dundee Grigol Sokhadze UK Javakhishvili Tbilisi State University Tbilisi Georgia Jagdish N. Srivastava Colorado State University Fort Collins, CO USA Héctor Manuel Zárate Solano Universidad Nacional de Colombia Banco de la República Bogotá Sinisa Stamatovic Colombia University of Montenegro Podgorica Montenegro Jasna Soldic-Aleksic Belgrade University Rade Stankic Belgrade Belgrade University Serbia Belgrade Serbia

Rabija Somun-Kapetanovic´ University of Sarajevo Robert G. Staudte Sarajevo La Trobe University Bosnia and Herzegovina Melbourne, VIC Australia

Roshini Sooriyarachchi David Steel University of Colombo University of Wollongong Colombo Wollongong, NSW Sri Lanka Australia List of Contributors liii

Jonathan C. Steele John D. Storey Minitab, Inc. Princeton University State College, PA Princeton, NJ USA USA

William E. Strawderman Gunnar Stefansson Rutgers University University of Iceland Newark, NJ Reykjavik USA Iceland

George P.H. Styan Michael A. Stephens McGill University Simon Fraser University Montréal, QC Burnaby, BC Canada Canada

Rolf Sundberg Stockholm University Czesław Ste˛pniak Maria Curie-Skłodowska University Stockholm Lublin Sweden Poland and Brajendra C. Sutradhar University of Rzeszów Memorial University Rzeszów St. John’s, NL Poland Canada

Stevan Stevic´ Elisabeth D. Svensson University of East Sarajevo Swedish Business School at Örebro University Republic of Srpska Örebro Bosnia and Herzegovina Sweden

Michail Sverchkov Theodor J. Stewart Bureau of Labor Statistics University of Cape Town Washington, DC Rondebosch USA South Africa and University of Manchester Jürgen Symanzik Manchester Utah State University UK Logan, UT USA

David W. Stockburger US Air Force Academy Barbara G. Tabachnick Missouri State University California State University Springfield, MO Northridge, CA USA USA liv List of Contributors

Carlos Eduardo Valdivieso Taborga Yves Tillé Universidad Privada Boliviana University of Neuchâtel Cochabamba Neuchâtel Bolivia Switzerland

Man Lai Tang David Todem Hong Kong Baptist University Michigan State University Kowloon East Lansing, MI Hong Kong USA

Masanobu Taniguchi Waseda University Roxana Toma Tokyo North Carolina State University Japan Raleigh, NC USA

Judith M. Tanur Stony Brook University Howell Tong Stony Brook, NY London School of Economics and Political Science USA London UK and Mark L. Taper National University of Singapore Montana State University Singapore Bozeman, MT Singapore USA

Henry C. Thode Matthias C. M. Troffaes Stony Brook University Durham University Stony Brook, NY Durham USA UK

Andrew C. Thomas Chris P.Tsokos Carnegie Mellon University University of South Florida Pittsburgh, PA Tampa, FL USA USA

Len Thomas Fugee Tsung University of St Andrews Hong Kong University of Science and Technology St Andrews Hong Kong UK China

Robert Tibshirani Stanford University Gerhard Tutz San Jose, CA Ludwig-Maximilians-Universität München USA Germany List of Contributors lv

Masayuki Uchida Vassiliy Voinov Osaka University Kazakhstan Institute of Management, Economics and Osaka Strategic Research Japan Almaty Kazakhstan

Hiroyuki Uesaka Osaka University Grace Wahba Osaka University of Wisconsin Japan Madison, WI USA Vladimir V. Ulyanov Lomonosov Moscow State University Moscow Chamont Wang Russia The College of New Jersey Ewing, NJ USA Cherubini Umberto University of Bologna Bologna Italy Charles C. Watson Watson Technical Consulting Savannah, GA Lev V. Utkin USA St. Petersburg State Forest Technical Academy St. Petersburg Russia Neville C. Weber University of Sydney Sydney, NSW Jordi Vallverdú Australia Universitat Autònoma de Barcelona Catalonia Spain William W. S. Wei Temple University Vasja Vehovar Philadelphia, PA University of Ljubljana USA Ljubljana Slovenia Alan H. Welsh Australian National University David Vere-Jones Canberra, ACT Victoria University of Wellington Australia Wellington New Zealand

Nanny Wermuth Reinhard Viertl Chalmers Technical University/University of Vienna University of Technology Gothenburg Vienna Gothenburg Austria Sweden lvi List of Contributors

Chris Wild Nakahiro Yoshida The University of Auckland University of Tokyo Auckland Tokyo New Zealand Japan

Susan R. Wilson Yasuto Yoshizoe University of New South Wales Aoyama Gakuin University Sydney, NSW Tokyo Australia Japan

Christopher Wlezien John C. Young Temple University Lake Charles, LA Philadelphia, PA USA USA

Timothy M. Young Douglas A. Wolfe University of Tennessee The Ohio State University Knoxville, TN Columbus, OH USA USA

Chong Ho Yu Yuehua Wu Arizona State University York University Tempe, AZ Toronto, ON USA Canada

Karl L. Wuensch Lotfi A. Zadeh East Carolina University University of California-Berkeley Greenville, NC Berkeley, CA USA USA

Janusz Wywial Michael A. Zazanis Katowice University of Economics Athens University of Economics and Business Katowice Athens Poland Greece

Yingcun Xia Raymond Zepp National University of Singapore Dewey International University Singapore Battambang Singapore Cambodia

Takeharu Yamanaka Zurab Zerakidze National Kyushu Cancer Center Javakhishvili Tbilisi State University Fukuoka Tbilisi Japan Georgia List of Contributors lvii

Anatoly Zhigljavsky Walter Zucchini School of Mathematics Georg-August-Universität Cardiff University Göttingen Cardiff Germany UK

Donald W. Zimmerman Nataša Kurnoga Živadinovic´ Carleton University University of Zagreb Ottawa, ON Zagreb Canada Croatia