Jerzy Neyman, 1894 - 1981

Erich Lehmann

Technical Report No. 155 May 1988

Research Supported by National Science Foundation Grant No. DMS84-01388

Department of Statistics University of Califomia Berkeley, California Jerzy Neyman, 1894 - 1981*

Early years. Jerzy Neyman was born in Bendery (Russia) to parents of Polish ances- try. His full name with title - Splawa-Neyman - the first part of which he dropped at age 30, reflects membership in the polish nobility. Neyman's father Czeslaw, who died when Jerzy was 12, was a lawyer and later judge, and an enthusiastic amateur archaeologist. Since the family had been prohibited by the Russian authorities from living in Central Poland, then under Russian domination, Neyman grew up in Russia: in Kherson, Melitopol, and Simferopol, and (after his father's death) in Kharkov, where in 1912 he entered the University. At Kharkov, Neyman was first interested in physics but because of his clumsiness in the Laboratory he abandoned it in favor of mathematics. On reading Lebesgue's "Lecons sur l'integration et la recherche des fonctions primitives", he later wrote (in Festschrift in honor of Herman Wold (1970)): "I became emotionally involved. I spent the summer of 1915 at a country estate, coaching the son of the owner. There were three summer houses on the estate, filled with young people, including girls whom I found beautiful and most attractive. However, the involvement with sets, measure and integration proved stronger than the charms of young ladies and most of my time was spent either in my room or on the adjacent balcony either on study or on my first efforst at new results, intended to fill in a few gaps that I found in Lebesgue". A manuscript on Lebesgue integration (500 pages, handwritten) that he submitted to a prize competition won a gold medal. One of his mentors at Kharkov was Serge Bernstein who lectured on probability theory and statistics (including application of the latter to agriculture), subjects that did not particularly interest Neyman. Nevertheless, he later acknowledged the influence of Bernstein from whom he "tried to acquire his tendency on concentrating on some 'big problem'." It was also Bernstein who introduced him to Karl Pearson's Grammar of Science, which made a deep impression. After the first World War, Poland regained its independence but soon became embroiled in a war with Russia over borders. Neyman was jailed as an enemy alien; in 1921, in an exchange of prisoners, he finally went to Poland for the first time at the age of 27.

* A condensed version of this report is scheduled to appear in a Supplement to the Dictionary of Scientific Biography. - 2 -

In Warsaw, he established contact with Sierpinski, one of the founders of the journal Fundamenta Mathematicae, which published one of Neyman's gold medal results (Vol.5 1923, 328-330). Although Neyman's heart was in pure mathematics, the statistics he had learned from Bernstein was more marketable and enabled him to obtain a position as (the only) statistician at the Agricultural Institute in Bydgoszcz (formerly Bromberg). There, during 1921/22, he produced several papers on the application of probabilistic ideas to agricultural experimentation. In the light of Neyman's later development, this work is of interest because of its introduction of probability models for the phenomena being studied, particularly a randomization model for the case of a completely randomized experiment. (For more details of Neyman's treatment see Scheff6, Ann. Math. Stat. 27 (1956) p.269.) He had learned the philosophy of such an approach from Karl Pearson's book, where great stress is laid on models as mental constructs whose formulation constitutes the essence of science.* In December 1922 Neyman gave up his job in Bydgoszcz to take charge of equip- ment and observations at the State Meteorological Institute, a change that enabled him to move to Warsaw. He did not like the work and soon left this position to become an Assistant at the University of Warsaw and Special Lecturer in mathematics and statistics at the Central College of Agriculture; he also gave regular lectures at the Univer- sity of Krakow. In 1924 he obtained his doctorate from the University of Warsaw with a thesis based on the papers he had written at Bydgoszcz. Since no one in Poland was able to gauge the importance of his statistical work (he was "suii generis", as he later described himself), the Polish authorities provided an opportunity for him to establish his credibility through publication in British journals. For this purpose they gave him a Fellowship to work with Karl Pearson in London. He did publish three papers in Biometrika (based in part on his earlier work), but scientifically the academic year (1925/26) spent in Pearson's Laboratory was a disappointment. Neyman found the work of the Laboratory old-fashioned and Pearson himself surprisingly ignorant of modern mathematics. (The fact that Pearson did not understand the difference between independence and lack of correlation led to a misunderstanding that nearly terminated Neyman's stay at the Laboratory.) So when, with the help of Pearson and Sierpinski, he received a Rockfeller Fellowship that made it possible for him to stay in the West for another year, he decided to spend it in Paris rather than in London.

*"'One of my favorite ideas", Neyman later wrote in 1957 (Rev. Int. Stat. Inst. 25, p.8), "learned from Mach via Karl Pearson's 'Grammar of Science', is that scientific theories are no more than models of natural phenomena". - 3 -

There he attended the lectures of Lebesgue and a seminar of Hadamard, "I felt that this was real mathematics worth studying" he wrote later, "and, were it not for Egon Pearson, I would have probably drifted to my earlier passion for sets, measure and integration, and returned to Poland as a faithful member of the Warsaw school and a steady contributor to Fundamenta Mathematicae."

The Neyman Pearson Theory. What pulled Neyman back into statistics was a letter he received in the Fall of 1926 from Egon Pearson, Karl Pearson's son, with whom Neyman had had only little contact in London. Egon had begun to question the rationale underlying some of the current work in statistics, and the letter outlined his concerns. Correspondence developed and, reinforced by occasional joint holidays, continued when at the end of the Rockefeller year Neyman returned to a hectic and difficult life in Warsaw. He continued to lecture at the University (as Docent after his habilitation in 1928), at the Central College of Agriculture, and at the University of Krakow. In addition, he founded a small statistical Laboratory at the Nencki Institute for Experimental Biology. To supplement his meager academic income, and to provide financial support for the young students and coworkers in his Laboratory, he took on a variety of consulting jobs. These involved different areas of application, with the majority coming from agriculture and from the Institute for Social Problems, the latter work being concerned with Polish census data. Neyman felt harassed, and his financial situation was always precarious. The bright spot in this difficult period was his work with the younger Pearson. Trying to find a unifying, logical basis which would lead systematically to the various statistical tests that had been proposed by Student and Fisher was a "big problem" of the kind for which he had hoped since his student days with Bernstein. In 1933 Karl Pearson retired from his chair at University College, London, and his position was divided between R.A. Fisher and Neyman's friend and collaborator Egon Pearson. The latter lost no time, and as soon as it became available, in the Spring of 1934 offered Neyman a temporary position in his Laboratory. Neyman was enthusiastic. This would greatly facilitate their joint work and bring relief to his Warsaw difficulties. The set of issues addressed in the joint work of Neyman and Pearson between 1926 and 1933 turned out indeed to be a "big problem," and their treatment of it established a new paradigm that changed the statistical landscape. What had concerned Pearson when he first approached Neyman in 1926 was the ad hoc nature of the small sample tests being studied by Fisher and Student. In his search for a general principle from which such tests could be derived, he had written to Student. Student in his reply had suggested that one would be inclined to reject a hypothesis under which the - 4 - observed sample is very improbable" if there is an alternative hypothesis which will explain the occurrence of the sample with a more reasonable probability." (E.S. Pear- son in "Research Papers in Statistics", F.N. David, Ed. 1966). This comment led Pearson to propose to Neyman the likelihood ratio criterion, in which the maximum likelihood of the observed sample under the alternatives under consideration is compared to its value under the hypothesis. During the next year Neyman and Pearson studied this and other approaches, and worked out likehood ratio tests for some important examples. They published their results in 1928 in a fundamental two-part paper, "On the use and interpretation of certain test criteria for purposes of statistical inference". The paper contained many of the basic concepts of what was to become the Neyman-Pearson Theory of Hypothesis Testing; such as the two types of error, the idea of power, and the distinction between simple and composite hypotheses. Although Pearson felt that the likelihood ratio provided the unified approach for which he had been looking, Neyman was not yet satisfied. It seemed to him that the likelihood principle itself was somewhat ad hoc and had no fully logical basis. How- ever, in February 1930, he was able to write Pearson that he had found "a rigorous argument in favour of the likelihood method". His new approach consisted of maximizing the power of the test, subject to the condition that under the hypothesis (assumed to be simple) the rejection probability has a preassigned value (the level of the test). He reassured Pearson that in all cases he had examined so far this logically convincing test coincided with the likelihood ratio test. A month later, Neyman announced to Pearson that he now had a general solution of the problem of testing a simple hypothesis against a simple alternative. The result in question is of course the "Fun- damental Lemma", which plays such a crucial role in Neyman-Pearson theory. The next step was to realize that in the case of more than one alternative there might exist a uniformly most powerful test that would simultaneously maximize the power for all of them. If such a test exists, Neyman found, it coincides with the likelihood ratio test but in the contrary case - alas - the likelihood ratio test may be biased. These results, together with many examples and elaborations, were published in 1933 under the title, "On the Problem of the Most Efficient Tests of Statistical Hypotheses". While in the 1928 paper the initiative and insights had been those of Pearson who had had to explain to Neyman what he was doing, the situation was now reversed with Neyman as leader and Pearson a somewhat reluctant follower. The 1933 paper is the fundamental paper in the theory of hypothesis testing. It established a framework for this theory* and states the problem of finding the best test * Its role in today's statistical climate is discussed in Lehmann, "The Neyman-Pearson theory after 50 years" (Proc. of the Berkeley Conference in honor of Jerzy Neyman and Jack Kiefer, Vol 1, 1-14. Wadsworth, 1985. - 5 - as a clearly formulated, logically convincing mathematical problem that one can then proceed to solve. Its importance transcends the theory of hypothesis testing since it provided also the inspiration for Wald's later, much more general statistical decision theory.

Survey sampling and confidence estimation. In the following year Neyman published another landmark paper. An elaboration of work on survey sampling he had done earlier for the Warsaw Institute for Social Problems, it was directed toward bringing clarity into a somewhat muddled discussion about the relative merits of two different sampling methods. His treatment, described by Fisher as "luminous", introduced many important concepts and results and may be said to have initiated the modern theory of survey sampling. The year 1935 brought two noteworthy events. The first was Neyman's appoint- ment to a permanent position of Reader (Assocciate Professor) in Pearson's Depart- ment. Although at the time he was still hoping eventually to return to Poland, he in fact never did except for brief visits. The second event was the presentation at a meeting of the Royal Statistical Society of an important paper on agricultural experimentation in which he raised some questions concerning Fisher's Latin Square design. This caused a break in their hitherto friendly relationship and was the beginning of lifelong disputes. (Fisher, who opened the discussion of the paper, stated that "he had hoped that Dr. Neyman's paper would be on a subject with which the author was fully acquainted, and on which he could speak with authority, as in the case of his address to the Society last summer. Since seeing the paper, he had come to the conclusion that Dr. Neyman had been somewhat unwise in his choice of topics".) Neyman was to remain in England for four years (1934-38). During this time he continued his collaboration with Egon Pearson on the theory and applications of optimal tests, efforts that also included contributions from graduate and postdoctoral students. To facilitate publication and to emphasize the unified point of view underlying this work, Neyman and Pearson set up a series, "Statistical Research Memoirs", published by University College and restricted to work done in the Department of Statistics. A first volume appeared in 1936, a second in 1938. Another central problem occupying Neyman during his London years was the theory of estimation: not point estimation in which a parameter is estimated by a unique number, but estimation by means of an interval or more general set in which the unknown parameter can be said to lie with specified confidence (i.e. probability). Such confidence sets are easily obtained under the Bayesian assumption that the parameter is itself random with known probability distribution, but Neyman's aim was to dispense with such an assumption which he considered arbitrary and unwarranted. - 6 -

Neyman published brief accounts of his solution to this problem in 1934 and 1935 and the theory in full generality in 1937 in "Outline of a Theory of Statistical Estima- tion Based on the Classical Theory of Probability" (Phil. Trans. Roy. Soc. Ser. A Vol.236, 333-380). He had first submitted this paper to Biometrika, then being edited by Egon Pearson, but to his great disappointment, Pearson had rejected it as too long and too mathematical. Neyman's approach was based on the idea of obtaining confidence sets S (X) for a parameter 0 from acceptance regions for the hypotheses that 0 = 00 by taking for S (X) the set of all parameter values 00 that would be accepted at the given level. This formulation established an equivalence between confidence sets and families of tests, and enabled him to transfer the test theory of the 1933 paper lock, stock, and barrel to the theory of estimation. (Unbeknownst to Neyman, the idea of obtaining confidence sets by inverting an acceptance rule had already been used in special cases by Laplace [in a large-sample binomial setting] and by Hotelling). In his paper on survey sampling, Neyman had referred to the relationship of his confidence intervals to Fisher's fiducial limits, which appeared to give the same results although derived from a somewhat different point of view. In the discussion of the paper, Fisher welcomed Neyman as an ally in the effort to free statistics from unwarranted Bayesian assumptions. He went on to say that "Dr. Neyman claimed to have generalized the argument of fiducial probability, and he had every reason to be proud of the line of argument he had developed for its perfect clarity. The generalization was a wide and very handsome one, but it had been erected at considerable expense,...". He then proceeded to indicate the disadvantages he saw in Neyman's formulation, of which perhaps the most important one (revealing the wide difference between their interpretations) was non-uniqueness. The debate between the two men over their respective approaches continued for many years, usually in less friendly terms; it is reviewed by Neyman in "Silver jubilee of my dispute with Fisher (J. Operat. Res. Soc. of Japan (1961) 145-154).

Statistical Philosophy. During the period of his work with Pearson, Neyman's attitude toward probability and hypothesis testing gradually underwent a radical change. In 1926, he tended to favor a Bayesian approach* in the belief that any theory would have to involve statements about the probabilities of various alternative hypotheses and hence an assumption of prior probabilities. In the face of Pearson's (and perhpas also * In Frequentist Probability and Frequentist Statistics (Synthese 36 (1977) 97-131, Neyman states, "I began as a quasi-Bayesian. My assumption was that the estimated parameter (just one!) is a particular value of a random variable having an unknown prior distribution." - 7 -

Fisher's) strongly anti-Bayesian position he became less certain, and in his papers of the late twenties (both alone and jointly with Pearson) he presented Bayesian and non- Bayesian approaches side by side. A decisive influence was von Mises' book "Wahrscheinlichkeit, Statistik und Wahrheit", (1928) about which he later wrote (in his Author's Note to A Selection of Early Statistical Papers of J. Neyman) that it "confirmed him as a radical 'frequentist' intent on probability as a mathematical ideal- ization of relative frequency". He opposed any subjective approach to science, and remained an avowed frequentist for the rest of his life. A second basic aspect of Neyman's work from the thirties on is a point of view, which he formulated clearly in the closing pages of his presentation at the 1937 Geneva Conference: "L'estimation statistique trait6e comme un probl'me classique de probabilit6" (Actual. Sci. et Industr. No 739, 25-57). His approach is not based on inductive reasoning, he states, but instead on the concept of "comportement inductif" or inductive behavior. That is, statistics is to be used not to extract from experience "beliefs" but as a guide to appropriate action. He summarized his views in a paragraph in a paper presented in 1949 to the Inter- national Congress on the Philosophy of Science. (Foundations of the General Theory of Estimation", Actual. Scie. et Industr. 1146 (1951) p. 85).

"Why abandon the phrase 'inductive reasoning' in favor of 'inductive behavior'? As explained in 1937*, the term inductive reasoning does not seem appropriate to describe the new method of estimation because all the reasoning behind this method is clearly deductive. Starting with whatever is known about the distribution of the observable variables X, we deduce the general form of the functions f(X) and g (X) which have the properties of confidence limits. Once a class of such pairs of functions is found, we formulate some properties of these functions which may be considered desirable and deduce either the existence or non-existence of an "optimum" pair, etc. Once the various possibilities are investigated we may decide to use a particular pair of confidence limits for purposes of statistical estimation. This decision, however, is not 'reasoning'. This is an act of will just as the decision to buy insurance is an act of will. Thus, the mental processes behind the new method of estimation consist of deductive reasoning and of an act of will. In these circumstances the term 'inductive reasoning' is out of place and, if one wants to keep the adjective 'inductive', it seems most appropriate to attach to it the noun 'behavior'.

* loc. cit. - 8 -

In other writings (for example in Rev. Internat. Statist. Inst. 25 (1957) 7-22), Ney- man acknowledges that a very similar point of view was advocated by Gauss and Laplace. It is of course also that of Wald's later general statistical decision theory. On the other hand, this view was strongly attacked by Fisher (for example in JRSS (B) 17 (1955) 69-78)) who maintained that decision making has no role in scientific inference, and that his fiducial argument provides exactly the mechanism required for this purpose.

Moving to America. By 1937, Neyman's work was becoming known not only in England and Poland but also in other parts of Europe and in America. He gave an invited talk about the theory of estimation at the International Congress of Probability held in 1937 in Geneva, and in the Spring of 1937 he spent six weeks in the United States on a lecture tour organized by S.S. Wilks. The visit included a week at the Graduate School of the Department of Agriculture in Washington arranged by Edward Deming. There he gave three lectures and six conferences on the relevance of probability theory to statistics, and on his work in hypothesis testing, estimation, sampling, and agricultural experimentation as illustrations of this approach. These "Lectures and Conferences on Mathematical Statistics", which provided a coherent statement of the new paradigm he had developed and exhibited its successful application to a number of substantive problems, were a tremendous success. A mimeographed version appeared in 1938 and was soon sold out. Neyman published an augmented second edition in 1952. After his return from the United States, Neyman debated whether to remain in England where he had a permanent position but little prospect of promotion and independence, or to return to Poland. Then completely unexpectedly, in the Fall of 1937 he received a letter from an unknown, G.C. Evans, chairman of the Mathematics Department at Berkeley, offering him a position in his department. Neyman hesitated for some time. California and its University were completely unknown quantities, while the situation in England - although not ideal - was reasonably satisfactory and stable. An attractive aspect of the Berkeley offer was the nonexistence there of any systematic program in statistics, so that he would be free to follow his own ideas. What finally tipped the balance in favor of Berkeley was the threat of war in Europe. Thus in April 1938 he decided to accept the Berkeley offer and emigrate to America, with his wife Olga (from whom he later separated) and his 2-year old son Michael. He had just turned 44, and he would remain in Berkeley for the rest of his long life.

The Berkeley Department of Statistics. Neyman's top priority after his arrival in Berkeley was the development of a statistics program, that is, a systematic set of - 9 -

courses and a faculty to teach therm He quickly organized a number of core courses and began to train some graduate students and one temporary instructor in his own approach to statistics. Administratively, he set up a Statistical Laboratory as a semi- autonomous unit within the Mathematics Department. However, soon America's entry into World War II in 1941 put all further academic development on hold. Neyman took on war work, and for the next years this became the Laboratory's central and all- consuming activity. The work dealt with quite specific military problems and did not produce results of lasting interest. The building of a faculty began in earnest after the war, and by 1956 Neyman had established a permanent staff of twelve members, many his own students, but also including three senior appointments from outside (Lobve, Scheff6, and Blackwell). Development of a substantial faculty, with the attendant problems of space, clerical staff, summer support, and so on, represented a major, sustained administrative effort. A crucial issue in the growth of the program concerned the course offerings in basic statistics by other departments. Although these involved major vested interests, Ney- man gradually concentrated the teaching of statistics within his statistics program, at least at the lower division level. This was an important achievement both in establish- ing the identity of his program and in obtaining the student base which alone could justify the ongoing expansion of the Faculty. In his negotiations with the Administra- tion, Neyman was strengthened by the growing international reputation of his Labora- tory, and by the increasing post-war importance of the field of statistics itself. An important factor in the Laboratory's reputation was the series of international "Symposia on Mathematical Statistics and Probability" that Neyman organized at 5- year intervals during 1945-1970, and the publication of their proceedings. The first Syposium was held in August 1945 to celebrate the end of the war and "the return to theoretical research" after years of war work. The meeting, although rather modest compared to the later symposia, was such a success that Neyman soon began to plan another one for 1950. In future years the Symposia grew in size, scope, and importance and did much to establish Berkeley as a major statistical center. The spectacular growth Neyman achieved for his group required a constant struggle with various administrative authorities including those of the Mathematics Department. To decrease the number of obstacles, and also to provide greater visibility for the statistics program, Neyman soon after his arrival in Berkeley began a long effort to obtain independent status for his group as a Department of Statistics. A separate Department finally became a reality in 1955, with Neyman as its chair. He resigned the chairmanship the following year (but retained the Directorship of the Laboratory to the end of his life). He felt, he wrote in his letter of resignation, that "the transformation of the old Statistical Laboratory into a Department of Statistics closed a period of - 10- development ... and opened a new phase." In these circumstances, he stated "it is only natural to have a new and younger man take over." There was perhaps another reason. Much of Neyman's energy during the nearly twenty years he had been in Berkeley had gone into administration. His efforts had been enormously successful: A first rate Departrnent, the Symposia, a large number of grants providing summer support for Faculty and students. It was a great accomplish- ment and his personal creation, but now it was time to get back more fully into research.

Applied Statistics. Neyman's theoretical research in Berkeley was largely motivated by his consulting work, one of the purposes for which the University had appointed him and through which he made himself useful to the campus at large. Problems in Astronomy, for example led to the interesting insight (1948, joint with Scott) that maximum likelihood estimates may cease to be consistent if the number of nuisance parameters tends to infinity with increasing sample size. Also, to simplify maximum likelihood computations, which in applications frequently became very cumbersome, he developed linearized, asymptotically equivalent methods - his BAN (best asymptotically normal) estimates (1949) - which have proved enormously. useful. His major research efforts in Berkeley were devoted to several large-scale applied projects. These included questions regarding competition of species (with T. Park), accident proneness (with G. Bates), the distribution of galaxies and the expansion of the Universe (with C.D. Shane and particularly Elizabeth Scott who became a steady collaborator and close companion), the effectiveness of cloud seeding, and a model for carcinogenesis. Of these perhaps the most important was the work in astronomy where the introduction of the Neyman-Scott clustering model brought new methods into the field which "were remarkable and perhaps have not yet been fully appreciated and exploited." (Peeble: Large Scale Structure of the Universe; Princeton Univ. Press, 1979). Neyman's applicational work, although it extends over many different areas, exhi- bits certain common features, which he made explicit in some of his writings and which combine into a philosophy for applied statistics. The following are some of the principal aspects. (1) The studies are indeterministic. Neyman has pointed out that the distinction between deterministic and indeterministic studies lies not so much in the nature of the phenomena as in the treatment accorded to them. ("Indeterminism in Science and new Demands on Statisticians". J. Amer. Statist. Assoc. 55 (1960) 625-639). In fact, many subjects that traditionally were treated as deterministic are now being viewed stochastically. Neyman himself has contributed to this change in several areas. - 11 -

(2) An indeterministic study of a scientific phenomenon involves the construction of a stochastic model. In this connection, Neyman introduced the important distinction between models that are interpolatory devices and those that embody genuine explanatory theories. The latter he describes as "a set of reasonable assumptions regarding the mechanism of the phenomena studied", while the former "by contrast consist of the selection of a relatively ad hoc family of functions, not deduced from underlying assumptions, and indexed by a set of parameters." (Stochastic Models and their Appli- cation to Social Phenomena", joint with W. Kruskal; presented at a joint session of IMS, ASA, and the Amer. Sociol. Soc., Sept. 1956.) The distinction is discussed earlier, and again later, in Neyman's papers in Ann. Math. Statist. 10 (1939) p.372/3 and in Reliability and Biometry. Siam. Philadelphia 1974, pp.185-188. Neyman's favorite examples of the distinction between the two types were the family of Pearson curves, which for a time was very popular as an interpolatory model that could be fitted to many different data sets, and Mendel's model for heredity. "At the time of its invention", he wrote about the latter in J. Amer. Statist. Assoc. 55(1960) 625-639) "this was little more than an interpolatory procedure invented to summarize Mendel's experiments with peas", but eventually it turned out to satisfy Neyman's two criteria for a model of genuine scientific value, namely (i) broad appli- cability (i.e. in Mendel's case not restricted to peas), and (ii) identifiability of details (the genes as entities with identifiable location on the chromosomes). Most actual modeling, Neyman points out, is intermediate between these two extremes, often exhibiting features of both kdnds. Related is the realization that inves- tigators will tend to use as building blocks models which "partly through experience and partly through imagination, appear to us familiar and, therefore, simple." ("Sto- chastic Models of Population Dynamics", Science 130 (1959) 303-308, joint with Scott). (3) To develop a 'genuine explanatory Theory' requires substantial knowledge of the scientific background of the problem. When the investigation concerns a branch of science with which the statistician is unfamiliar, this may require a considerable amount of work. For his collaboration with Scott in astronomy, Neyman studied the astrophysical literature, joined the American Astronomical Society, and became a member of the Commission on Galaxies of the International Astronomical Union. When he developed an interest in carcinogenesis, he spent three months at the National Institutes of Health to leam more about the biological background of the problem. Neyman summarizes his own attitude toward this kind of research in the closing sentence of his paper "A glance of my personal experiences in the process of research" (in Scientists at work (1970); Almquist and Wicksell): "The elements that are common ... seem to be my susceptibility to becoming emotionally involved in - 12 - other individuals' interests and enthusiasm, whether these individuals are sympathetic or not, and, particularly in the more recent decades, the delight I experience in trying to fathom the chance mechanisms of phenomena in the empirical world." An avenue for learning about the state of the art in a field and bringing together diverse points of view, which Neyman enjoyed and of which he made repeated use, was to arrange a conference. Two of these (on weather modification in 1965 and on molecular Biology in 1970) became parts of the then current Symposia. In addition, in 1961 jointly with Scott he arranged a "Conference on the Instability of Systems of Galaxies," and finally in July 1981, jointly with Le Cam and on very short notice, an Interdisciplinary Cancer Conference.

Epilogue. A month after the cancer conference, Neyman died of heart failure at age 87 on Aug. 5, 1981. He had been in reasonable health up to two weeks earlier, and on the day before his death was still working in the hospital on a book on weather modification.

Neyman is recognized as one of the founders of the modern theory of statistics, whose work on hypothesis testing, confidence intervals, and survey sampling has revo- lutionized both theory and practice. His enormous influence on the development of statistics is further greatly enhanced through the large number of his Ph. D. students. These are: From Poland: Kolodziejczyk, Iwaszkiewicz, Wilenski, Ptykowski

From London: Hsu, David, Johnson, Eisenhart, Sukhatme, Beall, Sato, Shanawany, Jack- son, Tang

From Berkeley: Chen, Dantzig, Lehmann, Massey, Fix, Chapman, Eudey, Gurland, Hodges, Seiden, Hughes, Taylor, Jeeves, Le Cam, Tate, Chiang, Agarwal, Sane, Read, Singh, Borgman, Marcus, Buehler, Kulkarni, Davies, Clifford, Samuels, Oyelese, Ray, Grieg, Green, Tsiatis, Singh, Javitz, Darden. His achievements were recognized by honorary degrees from the Universities of Chicago, California, Stockholm, and Warsaw, and from the Indian Statistical Institute. He was elected to the U.S. Academy of Sciences and to Foreign Membership in the - 13 -

Royal Society, the Royal Swedish Academy, and the Polish National Academy. In addition, he received many awards, including the U.S. National Medal of Science and the Guy Medal in Gold of the U.K. Royal Statistical Society. Neyman was completely and enthusiastically dedicated to his work, which filled his life - there was not time for hobbies. Work, however, included not only research and teaching, but also their social aspects such as traveling to meetings and organizing conferences. Pleasing his guests was an avocation; his hospitality had an international reputation. In his Laboratory he created a family atmosphere that included students, colleagues, and visitors, with himself as pater familias. As administrator, Neyman was indomitable. He would not take no for an answer, and was quite capable of resorting to unilateral actions. He firmly believed in the righteousness of his causes and found it difficult to understand how a reasonable per- son could disagree with him. At the same time, he had great charm that often was hard to resist. The characteristic that perhaps remains in mind above all is his generosity: further- ing the careers of his students, giving credit and doing more than his share in collaboration, and extending his help (including financial assistance out of his own pocket) to anyone who needed it. - 14 -

Bibliography.

I. Original works. A complete bibliography of Neyman's work is given at the end of David Kendall's Memoir (Biographical Memoirs of Fellows of the Royal Society, Vol. 28, 1982). Some of the early papers are reprinted in the two volumes, "A Selection of Early Sta- tistical papers of J. Neyman" and "Joint Statistical Papers of J. Neyman and E.S. Pearson" (University of California Press). Neyman's letters to E.S. Pearson from 1926-1933 (but not Pearson's replies) are preserved in Pearson's estate. An overall impression of Neyman's ideas and style can be gained from his book, "Lectures and Conferences on Mathematical Statistics and Probability", Second revised and enlarged edition (Graduate School U.S. Department of Agriculture, 1952). The following partial list provides a more detailed view of his major theoretical contributions: A. Paradigmatic Papers "On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference", Biometrika 20A (1928), 175-240; 263-294 (with E.S. Pearson). On the problem of the most efficient tests of statistical hypotheses. Phil. Trans. Roy. Soc. Lond. A 231, 1933, 289-337 (with E.S. Pearson). On the two different aspects of the representative method. J. Roy. Statist. Soc. 97, 1934, 558-625. (Spanish version of this paper appeared in Estadistica. J. Inter- Amer. Stat. Inst. 17, (1959) 587-651.) Outline of a theory of statistical estimation based on the classical theory of probability. Phil. Trans. Roy. Soc. Lond. A 203, 1937, 1211-1213.

B. Some other theoretical contributions. 'Smooth' test for goodness of fit. Skand. aktuar. Tidsskr. 20, 1937, 149-199. On a new class of 'contagious' distributions, applicable in entomology and bac- teriology. Ann. Math. Statist. 10, 1939, 35-57. Consistent estimates based on partially consistent observations. Econometrica 16, 1948, 1-32 (with E.L. Scott). Contribution to the theory of the chi-square test. Proc. Berkeley Symp. Math. Sta- tist. Probab. (ed. J. Neyman), pp.239-273. Berkeley: University of California Press. 1949. Optimal asymptotic tests of composite statistical hypotheses. Probability and statistics (The Harald Cramer Volume), (ed. U. Granander), pp.213-234. Uppsala, - 15 -

Sweden: Almquist & Wiksells. Outlier proneness of phenomena and of related distributions. Optimizing methods in statistics (ed. J.S. Rustagi), pp.413-430. New York and London: Academic Press Inc. 1971 (with E.L. Scott). Neyman's position regarding the role of statistics in science can be obtained from the following more philosophical and sometimes autobiographical articles. Foundation of the general theory of statistical estimation. Actual Scient. Ind. No. 1146, 83-95. 1951. The problem of inductive inference. Commun Pure Appl. Math. VII, 1955, 13-45. 'Inductive behavior' as a basic concept of philosophy of science. Revue Inst. Int. Statist. 2S, 1957, 7-22. Stochastic models of population dynamics. Science N.Y. 130, 1959, 303-308 (with E.L. Scott). A glance at some of my personal experiences in the process of research. Scientists at Work (ed. T. Dalenius. G. Karlsson & S. Malmquist), pp. 148-164. Uppsala, Sweden: Almquist & Wiksells. 1970. Frequentist probability and frequentist statistics. Synthiese 36, 1977, 97-131.

II. Secondary Literature. The most important source for Neyman's life and personality is Constance Reid, "Neyman - from Life" (Springer, 1982), which is based on Neyman's own recollec- tions (obtained during weekly meetings over a period of more than a year), those of his colleagues and former students, and on many original documents. A useful account of his collaboration with E.S. Pearson was written by Pearson for the Neyman Festschrift, "Research Papers in Statistics" (F.N. David, Ed., Wiley, 1966). Addi- tional accounts of his life and work are provided by the following papers: L. Le Cam and E.L. Lehmann, "J. Neyman - on the occasion of his 80-th birth- day". Ann. Statist. 2 (1974) vii-xiii. D.G. Kendall, M.S. Bartlett, and T.L. Page, "Jerzy Neman, 1894-1981" in Bio- graphical Memoirs of Fellows of the Royal Society 28 (1982) 379-412. E.L. Lehmann and Constance Reid, "In Memoriam - Jerzy Neyman, 1894-1981". The Amer. Statistician 36, (1982) 161/2. E.L. Scott, "Neyman, Jerzy" in Encycl. Statist. Sci. 6 (1985) 214-223. TECHNICAL REPORTS Statistics Department University of California, Berkeley 1. BREIMAN, L. and FREEDMAN, D. (Nov. 1981, revised Feb. 1982). How many variables should be entered in a regression equation? Jour. Amer. Statist. Assoc., March 1983, 78, No. 381, 131-136. 2. BRILLINGER, D. R. (Jan. 1982). Some contrasting examples of the time and frequency domain approaches to time series analysis. Time Series Methods in Hydrosciences, (A. H. El-Shaarawi and S. R. Esterby, eds.) Elsevier Scientific Publishing Co., Amsterdam, 1982, pp. 1-15. 3. DOKSUM, K. A. (Jan. 1982). On the performance of estimates in proportional hazard and log-linear models. Survival Analysis, (John Crowley and Richard A. Johnson, eds.) IMS Lecture Notes - Monograph Series, (Shanti S. Gupta. series ed.) 1982, 74-84. 4. BICKEL, P. J. and BREIMAN, L. (Feb. 1982). Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test. Ann. Prob., Feb. 1982, 11. No. 1, 185-214. 5. BRILLINGER, D. R. and TUKEY, J. W. (March 1982). Spectrum estimation and system identification relying on a Fourier transform. The Collected Works of J. W. Tukey, vol. 2, Wadsworth, 1985, 1001-1141. 6. BERAN, R. (May 1982). Jacklnife approximation to bootstrap estimates. Amn. Statist., March 1984, 12 No. 1, 101-118. 7. BICKEL, P. J. and FREEDMAN, D. A. (June 1982). Bootstrapping regression models with many parameters. Lehmann Festschrift, (P. J. Bickel, K. Doksum and J. L. Hodges, Jr., eds.) Wadsworth Press, Belmont, 1983, 2848. 8. BICKEL, P. J. and COLLINS, J. (March 1982). Minimizing Fisher information over mixtures of distributions. Sanhyl, 1983, 45, Series A, Pt. 1, 1-19. 9. BREIMAN, L. and FRIEDMAN, J. (July 1982). Estimating optimal transformations for multiple regression and correlation. 10. FREEDMAN, D. A. and PETERS, S. (July 1982, revised Aug. 1983). Bootstrapping a regression equation: some empirical results. JASA, 1984, 79, 97-106. 11. EATON, M. L. and FREEDMAN, D. A. (Sept. 1982). A remark on adjusting for covariates in multiple regression. 12. BICKEL, P. J. (April 1982). Minimax estimation of the mean of a mean of a normal distribution subject to doing well at a point. Recent Advances in Statistics, Academic Press, 1983. 14. FREEDMAN, D. A., ROTHENBERG, T. and SUTCH, R. (Oct. 1982). A review of a residential energy end use model. 15. BRILLINGER, D. and PREISLER, H. (Nov. 1982). Maximum likelihood estimation in a latent variable problem. Studies in Econometrics, Time Series, and Multivariate Statistics, (eds. S. Karlin, T. Amemiya, L. A. Goodman). Academic Press, New York, 1983, pp. 31-65. 16. BICKEL, P. J. (Nov. 1982). Robust regression based on infinitesimal neighborhoods. Ann. Statist., Dec. 1984, 12, 1349-1368. 17. DRAPER, D. C. (Feb. 1983). Rank-based robust analysis of linear models. I. Exposition and review. 18. DRAPER, D. C. (Feb 1983). Rank-based robust inference in regression models with several observations per cell. 19. FREEDMAN, D. A. and FIENBERG, S. (Feb. 1983, revised April 1983). Statistics and the scientific method, Comments on and reactions to Freedman, A rejoinder to Fienberg's comments. Springer New York 1985 Cohort Analysis in Social Research, (W. M. Mason and S. E. Fienberg, eds.). 20. FREEDMAN, D. A. and PETERS, S. C. (March 1983, revised Jan. 1984). Using the bootstrap to evaluate forecasting equations. J. of Forecasting. 1985, Vol. 4, 251-262. 21. FREEDMAN, D. A. and PETERS, S. C. (March 1983, revised Aug. 1983). Bootstrapping an econometric model: some empirical results. JBES, 1985, 2, 150-158. 22. FREEDMAN, D. A. (March 1983). Structural-equation models: a case study. 23. DAGGETT, R. S. and FREEDMAN, D. (April 1983, revised Sept. 1983). Econometrics and the law: a case study in the proof of antitrust damages. Proc. of the Berkeley Conference, in honor of Jerzy Neyman and Jack Kiefer. Vol I pp. 123-172. (L. Le Cam, R. Olshen eds.) Wadsworth, 1985. - 2 -

24. DOKSUM, K. and YANDELL, B. (April 1983). Tests for exponentiality. Handbook of Statistics, (P. R. Krishnaiah and P. K. Sen, eds.) 4, 1984. 25. FREEDMAN, D. A. (May 1983). Comments on a paper by Markus. 26. FREEDMAN, D. (Oct. 1983, revised March 1984). On bootstrapping two-stage least-squares estimates in stationary linear models. Anm. S 1984, 12,827-842. 27. DOKSUM, K. A. (Dec. 1983). An extension of partial likelihood methods for proportional hazard models to general transfornation models. Ann. Statist., 1987, 15, 325-345. 28. BICKEL, P. J., GOETZE, F. and VAN ZWET, W. R. (Jan. 1984). A simple analysis of third order efficiency of estimate Proc. of the Neyman-Kiefer Conference, (L. Le Cam, ed.) Wadsworth, 1985. 29. BICKEL, P. J. and FREEDMAN, D. A. Asymptotic normality and the bootstrap in stratified sampling. Amn. Statist. 12 470-482. 30. FREEDMAN, D. A. (Jan. 1984). The mean vs. the median: a case study in 4-R Act litigation. JBES. 1985 Vol 3 pp. 1-13. 31. STONE, C. J. (Feb. 1984). An asymptotically optimal window selection rule for kemel density estimates. Ann. Statist., Dec. 1984, 12, 1285-1297. 32. BREIMAN, L. (May 1984). Nail finders, edifices, and Oz. 33. STONE, C. J. (Oct. 1984). Additive regression and other nonparametric models. Ann. Statist., 1985, 13, 689-705. 34. STONE, C. J. (June 1984). An asymptotically optimal histogram selection rule. Proc. of the Berkeley Conf. in Honor of Jerzy Neyman and Jack Kiefer (L Le Cam and R. A. Olshen, eds.), II, 513-520. 35. FREEDMAN, D. A. and NAVIDL W. C. (Sept. 1984, revised Jan. 1985). Regression models for adjusting the 1980 Census. Statistical Science. Feb 1986, Vol. 1, No. 1, 3-39. 36. FREEDMAN, D. A. (Sept. 1984, revised Nov. 1984). De Finetti's theorem in continuous time. 37. DIACONIS, P. and FREEDMAN, D. (Oct. 1984). An elementary proof of Stirling's formula. Amer. Math Monthly. Feb 1986, Vol. 93, No. 2, 123-125. 38. LE CAM, L. (Nov. 1984). Sur l'approximation de familles de mesures par des families Gaussiennes. Ann. Inst. Henri Poincar6, 1985, 21, 225-287. 39. DIACONIS, P. and FREEDMAN, D. A. (Nov. 1984). A note on weak star uniformities. 40. BRELMAN, L. and IHAKA, R. (Dec. 1984). Nonlinear discrimiinant analysis via SCALING and ACE. 41. STONE, C. J. (Jan. 1985). The dimensionality reduction principle for generalized additive models. 42. LE CAM, L. (Jan. 1985). On the nornal approximation for sums of independent variables. 43. BICKEL, P. J. and YAHAV, J. A. (1985). On estimating the number of unseen species: how many executions were there? 44. BRILLINGER, D. R. (1985). The natural variability of vital rates and associated statistics. Biometrics, to appear. 45. BRILLINGER, D. R. (1985). Fourier inference: some methods for the analysis of array and nonGaussian series data. Water Resources Bulletin, 1985, 21, 743-756. 46. BREIMAN, L. and STONE, C. J. (1985). Broad spectrum estimates and confidence intervals for tail quantiles. 47. DABROWSKA, D. M. and DOKSUM, K. A. (1985, revised March 1987). Partial likelihood in transformation models with censored data. 48. HAYCOCK, K. A. and BRILLINGER. D. R. (November 1985). LIBDRB: A subroutine library for elementary time series analysis. 49. BRILLINGER, D. R. (October 1985). Fitting cosines: some procedures and some physical examples. Joshi Festschrift, 1986. D. Reidel. 50. BRILLINGER, D. R. (November 1985). What do seismology and neurophysiology have in common? - Statistics! Comptes Rendus Math. Acad. Sci. Canada. January, 1986. 51. COX, D. D. and O'SULLIVAN, F. (October 1985). Analysis of penalized likelihood-type estimators with application to generalized smoodting in Sobolev Spaces. - 3 -

52. O'SULLIVAN, F. (November 1985). A practical perspective on ill-posed inverse problems: A review with some new developments. To appear in Journal of Statistical Science. 53. LE CAM, L. and YANG, G. L. (November 1985, revised March 1987). On the preservation of local asymptotic normality under information loss. 54. BLACKWELL D. (November 1985). Approximate normality of large products. 55. FREEDMAN, D. A. (June 1987). As others see us: A case study in path analysis. Joumal of Educational Statistics. 12, 101-128. 56. LE CAM, L. and YANG, G. L. (January 1986). Replaced by No. 68. 57. LE CAM, L. (February 1986). On the Bernstein - von Mises theorem. 58. O'SULLIVAN, F. (January 1986). Estimation of Densities and Hazards by the Method of Penalized likelihood. 59. ALDOUS, D. and DIACONIS, P. (February 1986). Strong Uniform Times and Finite Random Walks. 60. ALDOUS, D. (March 1986). On the Markov Chain simulation Method for Unifonn Combinatorial Distributions and Simulated Annealing. 61. CHENG, C-S. (April 1986). An Optimization Problem with Applications to Optimal Design Theory. 62. CHENG, C-S., MAJUMDAR, D., STUFKEN, J. & TURE, T. E. (May 1986, revised Jan 1987). Optimal step type des'gn for comparing test treatments with a control. 63. CHENG, C-S. (May 1986, revised Jan. 1987). An Application of the Kiefer-Wolfowitz Equivalence Theorem. 64. O'SULLIVAN, F. (May 1986). Nonparametric Estimation in the Cox Proportional Hazards Model. 65. ALDOUS, D. (JUNE 1986). Finite-Time Implications of Relaxation Times for Stochastically Monotone Processes. 66. PrTMAN, J. (JULY 1986, revised November 1986). Stationary Excursions. 67. DABROWSKA, D. and DOKSUM, K. (July 1986, revised November 1986). Estimates and confidence intervals for median and mean life in the proportional hazard model with censored data. 68. LE CAM, L. and YANG, G.L. (July 1986). Distinguished Statistics, Loss of information and a theorem of Robert B. Davies (Fourth edition). 69. STONE, C.J. (July 1986). Asymptotic properties of logspline density estimation. 71. BICKEL, P.J. and YAHAV, J.A. (July 1986). Richardson Extrapolation and the Bootstrap. 72. LEHMANN, E.L. (July 1986). Statistics - an overview. 73. STONE, C.J. (August 1986). A nonparametric framework for statistical modelling. 74. BIANE, PH. and YOR, M. (August 1986). A relation between L6vy's stochastic area formula, Legendre polynomial, and some continued fractions of Gauss. 75. LEHMANN, E.L. (August 1986, revised July 1987). Comparing Location Experiments. 76. O'SULLIVAN, F. (September 1986). Relative risk estimation. 77. O'SULLIVAN, F. (September 1986). Deconvolution of episodic hormone data. 78. PITMAN, J. & YOR, M. (September 1987). Further asymptotic laws of planar Brownian motion. 79. FREEDMAN, D.A. & ZEISEL, H. (November 1986). From mouse to man: The quantitative assessment of cancer risks. To appear in Statistical Science. 80. BRILLINGER, D.R. (October 1986). Maximum likelihood analysis of spike trains of interacting nerve cells. 81. DABROWSKA, D.M. (November 1986). Nonparametric regression with censored survival time data. 82. DOKSUM, K.J. and LO, A.Y. (November 1986). Consistent and robust Bayes Procedures for Location based on Partial Infonnation. 83. DABROWSKA, D.M., DOKSUM, KA. and MIURA, R. (November 1986). Rank estimates in a class of semiparametric two-sample models. - 4 -

84. BRILLINGER, D. (Deember 1986). Some statistical methods for random process data from seismology and neurophysiology. 85. DIACONIS, P. and FREEDMAN, D. (December 1986). A dozen de Finetti-style results in search of a theory. Ann. Inst. Henri Poincar, 1987, 23, 397-423. 86. DABROWSKA, D.M. (January 1987). Uniform consistency of nearest neighbour and kemel conditional Kaplan - Meier estimates. 87. FREEDMAN, DA., NAVIDI, W. and PETERS, S.C. (February 1987). On the impact of variable selection in fitting regression equations. 88. ALDOUS, D. (February 1987, revised April 1987). Hashing with linear probing, under non-uniform probabilities. 89. DABROWSKA, D.M. and DOKSUM, K.A. (March 1987, revised January 1988). Estimating and testing in a two sample generalized odds rate model. 90. DABROWSKA, D.M. (March 1987). Rank tests for matched pair experiments with censored data. 91. DIACONIS, P and FREEDMAN, D.A. (April 1988). Conditional limit theorems for exponential families and finite versions of de Finetti's theorem. To appear in the Journal of Applied Probability. 92. DABROWSKA, D.M. (April 1987, revised September 1987). Kaplan-Meier estimate on the plane. 92a. ALDOUS, D. (April 1987). The Harmonic mean formula for probabilities of Unions: Applications to sparse random graphs. 93. DABROWSKA, D.M. (June 1987, revised Feb 1988). Nonparametric quantile regression with censored data. 94. DONOHO, D.L. & STARK, PJB. (June 1987). Uncertainty principles and signal recovery. 95. CANCELLED 96. BRILLINGER, D.R. (June 1987). Some examples of the statistical analysis of seismological data. To appear in Proceedings, Centennial Anniversary Symposium, Seismographic Stations, University of California, Berkeley. 97. FREEDMAN, DA. and NAVIDI, W. (June 1987). On the multi-stage model for carcinogenesis. To appear in Envirormental Health Perspectives. 98. O'SULLIVAN, F. and WONG, T. (June 1987). Determining a function diffusion coefficient in the heat equation. 99. O'SULLIVAN, F. (June 1987). Constrained non-linear regularization with application to some system identification problems. 100. LE CAM, L. (July 1987, revised Nov 1987). On the standard asymptotic confidence ellipsoids of Wald. 101. DONOHO, D.L. and LIU, R.C. (July 1987). Pathologies of some minimum distance estimators. Annals of Statistics, June, 1988. 102. BRILLINGER, D.R., DOWNING, K.H. and GLAESER, R.M. (July 1987). Some statistical aspects of low-dose electron imaging of crystals. 103. LE CAM, L. (August 1987). Harald Cramer and sums of independent random variables. 104. DONOHO, A.W., DONOHO, D.L. and GASKO, M. (August 1987). Macspin: Dynamic graphics on a desktop computer. IEEE Computer Graphics and applications, June, 1988. 105. DONOHO, D.L. and LIU, R.C. (August 1987). On minimax estimation of linear functionals. 106. DABROWSKA, D.M. (August 1987). Kaplan-Meier estimate on the plane: weak convergence, LIL and the bootstrap. 107. CHENG, C-S. (August 1987). Some orthogonal main-effect plans for asymmetrical factorials. 108. CHENG, C-S. and JACROUX, M. (August 1987). On the construction of trend-free run orders of two-level factorial designs. 109. KLASS, M.J. (August 1987). Maximizing E max S / ES': A prophet inequality for sums of I.I.D. mean zero variates. 110. DONOHO, D.L. and LIU, R.C. (August 1987). The "automatic" robustness of minimum distance functionals. Armals of Statistics, June, 1988. 111. BICKEL P.J. and GHOSH, J.K. (August 1987, revised June 1988). A decomposition forte likelihood ratio statistic and the Bartlett correction - a Bayesian argument. - 5 -

112. BURDZY, K., PiTMAN, J.W. and YOR, M. (September 1987). Some asymptotic laws for crossings and excursions. 113. ADHIKARI, A. and P1TMAN, J. (September 1987). The shortest planar arc of width 1. 114. RITOV, Y. (September 1987). Estimation in a linear regression model with censored data. 115. BICKEL, P.J. and RITOV, Y. (SepL 1987, revised Aug 1988). Large sample theory of estimation in biased sampling regression models I. 116. RITOV, Y. and BICKEL, P.J. (Sept.1987, revised Aug. 1988). Achieving information bounds in non and semiparametric models. 117. RITOV, Y. (October 1987). On the convergence of a maximal correlation algorithm with alternating projections. 118. ALDOUS, D.J. (October 1987). Meeting times for independent Markov chains. 119. HESSE, C.H. (October 1987). An asymptotic expansion for the mean of the passage-time distribution of integrated Brownian Motion. 120. DONOHO, D. and LIU, R. (October 1987, revised March 1988). Geometrizing rates of convergence, I1. 121. BRILLINGER, D.R. (October 1987). Estimating the chances of large earthquakes by radiocarbon dating and statistical modelling. To appear in Statistics a Guide to the Unknown. 122. ALDOUS, D., FLANNERY, B. and PALACIOS, J.L. (November 1987). Two applications of um processes: The fringe analysis of search trees and the simulation of quasi-stationary distributions of Markov chains. 123. DONOHO, D.L., MACGIBBON, B. and LIU, R.C. (Nov.1987, revised July 1988). Minimax risk for hyperrectangles. 124. ALDOUS, D. (November 1987). Stopping times and tightness II. 125. HESSE, C.H. (November 1987). The present state of a stochastic model for sedimentation. 126. DALANG, R.C. (December 1987, revised June 1988). Optimal stopping of two-parameter processes on nonstandard probability spaces. 127. Same as No. 133. 128. DONOHO, D. and GASKO, M. (December 1987). Multivariate generalizations of the median and trimmed mean II. 129. SMITH, D.L. (December 1987). Exponential bounds in Vapnik-tervonenkis classes of index 1. 130. STONE, C.J. (Nov.1987, revised Sept. 1988). Uniform error bounds involving logspline models. 131. Same as No. 140 132. HESSE, C.H. (December 1987). A Bahadur - Type representation for empirical quantiles of a large class of stationary, possibly infinite - variance, linear processes 133. DONOHO, D.L. and GASKO, M. (December 1987). Multivariate generalizations of the median and trimmed mean, I. 134. DUBINS, L.E. and SCHWARZ, G. (December 1987). A sharp inequality for martingales and stopping-times. 135. FREEDMAN, D.A. and NAVIDI, W. (December 1987). On the risk of lung cancer for ex-smokers. 136. LE CAM, L. (January 1988). On some stochastic models of the effects of radiation on cell survival. 137. DIACONIS, P. and FREEDMAN, D.A. (April 1988). On the uniform consistency of Bayes estimates for multinomial probabilities. 137a. DONOHO, D.L. and LIU, R.C. (1987). Geometrizing rates of convergence, I. 138. DONOHO, D.L. and LIU, R.C. (January 1988). Geometrizing rates of convergence, HI. 139. BERAN, R. (January 1988). Refining simultaneous confidence sets. 140. HESSE, C.H. (December 1987). Numerical and statistical aspects of neural networks. 141. BRILLINGER, D.R. (January 1988). Two reports on trend analysis: a) An Elementary Trend Analysis of Rio Negro Levels at Manaus, 1903-1985 b) Consistent Detection of a Monotonic Trend Superposed on a Stationary Time Series 142. DONOHO, D.L. (Jan. 1985, revised Jan. 1988). One-sided inference about functionals of a density. - 6 -

143. DALANG, R.C. (February 1988). Randomization in the two-armed bandit problem. 144. DABROWSKA, D.M., DOKSUM, KA. and SONG, J.K. (February 1988). Graphical comparisons of cumulative hazards for two populations. 145. ALDOUS, D.J. (February 1988). Lower bounds for covering times for reversible Markov Chains and random walks on graphs. 146. BICKEL, P.J. and RITOV, Y. (Feb.1988, revised August 1988). Estimating integrated squared density derivatives. 147. STARK, P.R. (March 1988). Strict bounds and applications. 148. DONOHO, D.L. and STARK, P.B. (March 1988). Rearrangements and smoothing. 149. NOLAN, D. (March 1988). Asymptotics for a multivariate location estimator. 150. SEILLEER, F. (March 1988). Sequential probability forecasts and the probability integral transfonn. 151. NOLAN, D. (March 1988). Limit theorems for a random convex set. 152. DIACONIS, P. and FREEDMAN, DA. (April 1988). On a theorem of Kuchler and Lauritzen. 153. DIACONIS, P. and FREEDMAN, D.A. (April 1988). On the problem of types. 154. DOKSUM, KA. (May 1988). On the correspondence between models in binary regression analysis and survival analysis. 155. LEHMANN, E.L. (May 1988). Jerzy Neyman, 1894-1981. 156. ALDOUS, D.J. (May 1988). Stein's method in a two-dimensional coverage problem. 157. FAN, J. (June 1988). On the optimal rates of convergence for nonparametric deconvolution problem. 158. DABROWSKA, D. (June 1988). Signed-rank tests for censored matched pairs. 159. BERAN, R.J. and MILLAR, P.W. (June 1988). Multivariate symmetry models. 160. BERAN, R.J. and MILLAR, P.W. (June 1988). Tests of fit for logistic models. 161. BREIMAN, L. and PETERS, S. (June 1988). Comparing automatic bivariate smoothers (A public service enterprise). 162. FAN, J. (June 1988). Optimal global rates of convergence for nonparametric deconvolution problem. 163. DIACONIS, P. and FREEDMAN, DA. (June 1988). A singular measure which is locally uniform. 164. BICKEL, P.J. and KREEGER, A.M. (July 1988). Confidence bands for a distribution function using the bootstrap. 165. HESSE, C.H. (July 1988). New methods in the analysis of economic time series I. 166. FAN, JIANQING (July 1988). Nonparametric estimation of quadratic functionals in Gaussian white noise. 167. BREIMAN, L., STONE, C.J. and KOOPERBERG, C. (August 1988). Confidence bounds for extreme quantiles. 168. LE CAM, L. (August 1988). Maximum likelihood an introduction. 169. BREIMAN, L. (August 1988). Submodel selection and evaluation in regression-The conditional case and little bootstrap. 170. LE CAM, L. (September 1988). On the Prokhorov distance between the empirical process and the associated Gaussian bridge. 171. STONE, C.J. (September 1988). Large-sample inference for logspline models. 172. ADLER, R.J. and EPSTEIN, R. (September 1988). Intersection local times for infinite systems of planar brownian motions and for the brownian density process. 173. MILLAR, P.W. (October 1988). Optimal estimation in the non-parametric multiplicative intensity model. 174. YOR, M. (October 1988). Interwinings of Bessel processes. 175. ROJO, J. (October 1988). On the concept of tail-heaviness. Copies of these Reports plus the most recent additions to the Technical Report series are available from the Statistics Department technical typist in room 379 Evans Hall or may be requested by mail from: Department of Statistics University of Califomia Berkeley, Califomia 94720 Cost: $1 per copy.