DOCSLIB.ORG

STATISTICAL SCIENCE Volume 31, Number 3 August 2016

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

STATISTICAL SCIENCE Volume 31, Number 3 August 2016 A Review of Nonparametric Hypothesis Tests of Isotropy Properties in Spatial Data ...................................................Zachary D. Weller and Jennifer A. Hoeting 305 Rank Tests from Partially Ordered Data Using Importance and MCMC Sampling Methods .........................................................Debashis Mondal and Nina Hinrichs 325 On Negative Outcome Control of Unobserved Confounding as a Generalization of Difference-in-Differences................Tamar Sofer, David B. Richardson, Elena Colicino, Joel Schwartz and Eric J. Tchetgen Tchetgen 348 Quantum Annealing with Markov Chain Monte Carlo Simulations and D-Wave Quantum Computers...........................................Yazhen Wang, Shang Wu and Jian Zou 362 MarkovChainsasModelsinStatisticalMechanics.............................Eugene Seneta 399 Fractional Imputation in Survey Sampling: A Comparative Review ...............................................................Shu Yang and Jae Kwang Kim 415 AConversationwithMichaelWoodroofe............Moulinath Banerjee and Bodhisattva Sen 433 AConversationwithArthurCohen...............................................Joseph Naus 442 AConversationwithEstateV.Khmaladze................... Hira L. Koul and Roger Koenker 453 Statistical Science [ISSN 0883-4237 (print); ISSN 2168-8745 (online)], Volume 31, Number 3, August 2016. Published quarterly by the Institute of Mathematical Statistics, 3163 Somerset Drive, Cleveland, OH 44122, USA. Periodicals postage paid at Cleveland, Ohio and at additional mailing offices. POSTMASTER: Send address changes to Statistical Science, Institute of Mathematical Statistics, Dues and Subscriptions Office, 9650 Rockville Pike—Suite L2310, Bethesda, MD 20814-3998, USA. Copyright © 2016 by the Institute of Mathematical Statistics Printed in the United States of America EDITOR Peter Green University of Bristol and University of Technology, Sydney ASSOCIATE EDITORS Steve Buckland Byron Morgan Eric Tchetgen Tchetgen University of St. Andrews University of Kent Harvard School of Public Jiahua Chen Peter Müller Health University of British Columbia University of Texas Yee Whye Teh Rong Chen Sonia Petrone University of Oxford Rutgers University Bocconi University Jon Wakefield Rainer Dahlhaus Nancy Reid University of Washington University of Heidelberg University of Toronto Guenther Walther Peter J. Diggle Glenn Shafer Stanford University Lancaster University Rutgers Business Jon Wellner Robin Evans School–Newark and University of Washington University of Oxford New Brunswick Martin Wells Michael Friendly Royal Holloway College, Cornell University York University University of London Tong Zhang Edward I. George Michael Stein Rutgers University University of Pennsylvania University of Chicago MANAGING EDITOR T. N. Sriram University of Georgia PRODUCTION EDITOR Patrick Kelly EDITORIAL COORDINATOR Kristina Mattson PAST EXECUTIVE EDITORS Morris H. DeGroot, 1986–1988 Morris Eaton, 2001 Carl N. Morris, 1989–1991 George Casella, 2002–2004 Robert E. Kass, 1992–1994 Edward I. George, 2005–2007 Paul Switzer, 1995–1997 David Madigan, 2008–2010 Leon J. Gleser, 1998–2000 Jon A. Wellner, 2011–2013 Richard Tweedie, 2001 Statistical Science 2016, Vol. 31, No. 3, 305–324 DOI: 10.1214/16-STS547 © Institute of Mathematical Statistics, 2016 A Review of Nonparametric Hypothesis Tests of Isotropy Properties in Spatial Data Zachary D. Weller and Jennifer A. Hoeting Abstract. An important aspect of modeling spatially referenced data is ap- propriately specifying the covariance function of the random field. A practi- tioner working with spatial data is presented a number of choices regarding the structure of the dependence between observations. One of these choices is to determine whether or not an isotropic covariance function is appropri- ate. Isotropy implies that spatial dependence does not depend on the direc- tion of the spatial separation between sampling locations. Misspecification of isotropy properties (directional dependence) can lead to misleading infer- ences, for example, inaccurate predictions and parameter estimates. A re- searcher may use graphical diagnostics, such as directional sample vari- ograms, to decide whether the assumption of isotropy is reasonable. These graphical techniques can be difficult to assess, open to subjective interpreta- tions, and misleading. Hypothesis tests of the assumption of isotropy may be more desirable. To this end, a number of tests of directional dependence have been developed using both the spatial and spectral representations of random fields. We provide an overview of nonparametric methods available to test the hypotheses of isotropy and symmetry in spatial data. We discuss important considerations in choosing a test, provide recommendations for implement- ing a test, compare several of the methods via a simulation study, and propose a number of open research questions. Several of the reviewed methods can be implemented in R using our package spTest, available on CRAN. Key words and phrases: Isotropy, symmetry, nonparametric spatial covari- ance. REFERENCES MR3316189 BANERJEE,S.,CARLIN,B.P.andGELFAND, A. E. (2014). Hi- BACZKOWSKI, A. J. (1990). A test of spatial isotropy. In Compstat erarchical Modeling and Analysis for Spatial Data. CRC Press, 277–282. Springer, Berlin. Boca Raton, FL. BACZKOWSKI,A.J.andMARDIA, K. V. (1987). Approxi- BORGMAN,L.andCHAO, L. (1994). Estimation of a multidimen- mate lognormality of the sample semivariogram under a Gaus- sional covariance function in case of anisotropy. Math. Geol. 26 sian process. Comm. Statist. Simulation Comput. 16 571–585. 161–179. MR1267007 MR0903164 BOWMAN,A.W.andAZZALINI, A. (2014). R package sm: Non- BACZKOWSKI,A.J.andMARDIA, K. V. (1990). A test of spa- parametric smoothing methods (version 2.2-5.4), Univ. Glas- tial symmetry with general application. Comm. Statist. Theory gow, UK and Univ. di Padova, Italia. Methods 19 555–572. MR1067588 BOWMAN,A.W.andCRUJEIRAS, R. M. (2013). Inference for BANDYOPADHYAY,S.,LAHIRI,S.N.andNORDMAN,D.J. variograms. Comput. Statist. Data Anal. 66 19–31. MR3064021 (2015). A frequency domain empirical likelihood method for CABAÑA, E. M. (1987). Affine processes: A test of isotropy based irregularly spaced spatial data. Ann. Statist. 43 519–545. on level sets. SIAM J. Appl. Math. 47 886–891. MR0898839 Zachary D. Weller is Ph.D. Candidate, Department of Statistics, Colorado State University, Fort Collins, Colorado 80523-1877, USA (e-mail: [email protected]). Jennifer A. Hoeting is Professor, Department of Statistics, Colorado State University, Fort Collins, Colorado 80523-1877, USA (e-mail: [email protected]). CHORTI,A.andHRISTOPULOS, D. T. (2008). Nonparametric JONA-LASINIO, G. (2001). Modeling and exploring multivariate identification of anisotropic (elliptic) correlations in spatially spatial variation: A test procedure for isotropy of multivariate distributed data sets. IEEE Trans. Signal Process. 56 4738– spatial data. J. Multivariate Anal. 77 295–317. MR1838690 4751. MR2517209 JOURNEL,A.G.andHUIJBREGTS, C. J. (1978). Mining Geo- CRESSIE, N. A. C. (1993). Statistics for Spatial Data. Wiley, New statistics. Academic Press, New York. York. MR1239641 JUN,M.andGENTON, M. G. (2012). A test for stationarity of ECKER,M.D.andGELFAND, A. E. (1999). Bayesian modeling spatio-temporal random fields on planar and spherical domains. and inference for geometrically anisotropic spatial data. Math. Statist. Sinica 22 1737–1764. MR3027105 Geol. 31 67–83. KIM,T.Y.andPARK, J. (2012). On nonparametric variogram es- ECKER,M.D.andGELFAND, A. E. (2003). Spatial modeling and timation. J. Korean Statist. Soc. 41 399–413. MR3255345 predication under stationary non-geometric range anisotropy. LAHIRI, S. N. (2003). Resampling Methods for Dependent Data. Environ. Ecol. Stat. 10 165–178. MR1982482 Springer, New York. MR2001447 FUENTES, M. (2005). A formal test for nonstationarity of spa- LAHIRI,S.N.andZHU, J. (2006). Resampling methods for spa- tial stochastic processes. J. Multivariate Anal. 96 30–54. tial regression models under a class of stochastic designs. Ann. MR2202399 Statist. 34 1774–1813. MR2283717 FUENTES, M. (2006). Testing for separability of spatial–temporal LI,B.,GENTON,M.G.andSHERMAN, M. (2007). A nonpara- covariance functions. J. Statist. Plann. Inference 136 447–466. metric assessment of properties of space–time covariance func- MR2211349 tions. J. Amer. Statist. Assoc. 102 736–744. MR2370863 FUENTES, M. (2007). Approximate likelihood for large irregu- LI,B.,GENTON,M.G.andSHERMAN, M. (2008a). Testing the larly spaced spatial data. J. Amer. Statist. Assoc. 102 321–331. covariance structure of multivariate random fields. Biometrika MR2345545 95 813–829. MR2461213 FUENTES, M. (2013). Spectral methods. Wiley StatsRef: Statistics LI,B.,GENTON,M.G.andSHERMAN, M. (2008b). On the Reference Online. asymptotic joint distribution of sample space–time covariance FUENTES,M.andREICH, B. (2010). Spectral domain. In Hand- estimators. Bernoulli 14 228–248. MR2401661 book of Spatial Statistics 55–77. CRC Press, Boca Raton, FL. LU, H. (1994). On the distributions of the sample covariogram and GARCÍA-SOIDÁN, P. (2007). Asymptotic normality of the semivariogram and their use in testing for isotropy. Ph.D. thesis, Nadaraya–Watson semivariogram estimators. TEST 16 479– Univ. Iowa. 503. MR2365173 LU,H.andZIMMERMAN, D. L. (2001). Testing for isotropy GARCÍA-SOIDÁN,P.H.,FEBRERO-BANDE,M.andGONZÁLEZ- and other directional symmetry properties of spatial correlation.
Recommended publications
  • Program Book Final

    Program Book Final

    GENERAL PROGRAM SCHEDULE 8:00 am–12:00 pm FRY-New Brunswick SUNDAY AUGUST 8 Advisory Committee on Teacher Enhancement (closed) Committee/Business Meetings & Other Activities Chair(s): Thomas H. Short, Indiana University of Pennsylvania 7:00 am–4:00 pm FRY-Meeting Services Desk 8:00 am–12:30 pm ICH-Halton JSM CE Pre-registered Pick Up Desk Committee on Publications (closed) Chair(s): William Q. Meeker, Iowa State University 7:00 am–6:00 pm FRY- Prince Edward Island Sunday Speaker Work Room 8:00 am–1:00 pm FRY-York Pathways to the Future Workshop 7:00 am–6:00 pm TCC-702 Organizer(s): Lynne Billard, University of Georgia Speaker Work Room 8:00 am–6:00 pm TCC-Exhibit Hall E 7:00 am–8:30 pm TCC-600 Level Exhibitor Lounge ASA Membership Booth (Reg Area) 9:00 am–10:30 am ICH-Grenadier 7:00 am–8:30 pm TCC-600 Level Caucus for Women in Statistics Committee Meeting JSM Main Registration Organizer(s): Mariza de Andrade, Mayo Clinic 7:00 am–8:30 pm TCC-600 Level 9:00 am–11:00 am TCC-Exhibit Hall F Special Assistance Desk Career Placement Service (Job Posting and Resume Submission Only) 7:00 am–8:30 pm TCC-Entrance of South Building Guest Services Desk 9:00 am–12:00 pm FRY-Nova Scotia Council of Sections Governing Board Meeting 7:00 am–8:30 pm TCC-600 Level (closed) Press Desk Chair(s): Thomas J. Santner, The Ohio State University 7:00 am–11:00 pm TCC-600 Level 9:00 am–5:00 pm TCC-600 Level Cyber Café and Message Center ASA Marketplace 7:30 am–8:15 am ICH-Oakville 10:00 am–2:00 pm ICH-Haliburton Association of GCRC Statisticians Breakfast (closed) Committee on Meetings (closed) Organizer(s): Curtis A Parvin, Washington University School of Medicine Chair(s): Kim McGuigan, Medco Health Solutions 7:30 am–9:00 am ICH-Grenadier 11:00 am–2:00 pm ICH-Humber Committee on Women in Statistics (closed) NISS/SAMSI Affiliates Meeting (closed) Chair(s): Amita K.
  • Notices of the American Mathematical Society

    Notices of the American Mathematical Society

    NUMERICAL ANALYSIS edited by Gene H. Golub and Joseph Oliger Lecture Notes from the Short Course sponsored by the AMS, Atlanta, january 3-4, 1978 This is the collection of texts prepared by the lec­ corporate the classical notions and realistic costs turers of the Numerical Analysis Short Course of producing the desired result. The discussion of given at the A. M.S. meeting in Atlanta, Georgia in good vs. best approximation is an example. More January 1978. Computational linear algebra, opti· attention is being given to providing not only an mization and the solution of nonlinear equations, answer, but a computed guarantee that it is a good the approximation of functions and functionals, answer-or a poor one. Easily computed and sharp and approximations for initial and boundary value a posteriori estimates are needed. The discussion problems for ordinary and partial differential equa­ of estimates of condition numbers is an example. tions are discussed. Methods such as the QR fac­ There is progress being made in algorithm design torization, singular value decomposition, quasi­ based on operator splittings which allow one to Newton and secant methods, finite difference, fi· take advantage of being able to solve simpler sub­ nite element and collocation methods are included problems very efficiently. Updating strategies for in these discussions. · optimization and splitting methods for differential equations are examples. The subject matter was chosen to emphasize prom­ inent research areas and attitudes in numerical These texts should be useful to the practicing users analysis. These are introductory lectures on the of numerical methods, programmers, scientists, subject matter for presentation to an audience of and engineers who would like to know what prog· scientists from other areas or disciplines.
  • Recent Developments in Nonparametric Inference and Probability Festschrift for Michael Woodroofe

    Recent Developments in Nonparametric Inference and Probability Festschrift for Michael Woodroofe

    Institute of Mathematical Statistics LECTURE NOTES–MONOGRAPH SERIES Recent Developments in Nonparametric Inference and Probability Festschrift for Michael Woodroofe Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page, Editors Volume 50 ISBN 0-940600-66-9 Institute of Mathematical Statistics LECTURE NOTES–MONOGRAPH SERIES Volume 50 Recent Developments in Nonparametric Inference and Probability Festschrift for Michael Woodroofe Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page, Editors Institute of Mathematical Statistics Beachwood, Ohio, USA Institute of Mathematical Statistics Lecture Notes–Monograph Series Series Editor: R. A. Vitale The production of the Institute of Mathematical Statistics Lecture Notes–Monograph Series is managed by the IMS Office: Jiayang Sun, Treasurer and Elyse Gustafson, Executive Director. Library of Congress Control Number: 2006934183 International Standard Book Number 0-940600-66-9 International Standard Serial Number 0749-2170 Copyright c 2006 Institute of Mathematical Statistics All rights reserved Printed in the United States of America Contents Preface Jiayang Sun, Anirban DasGupta, Vince Melfi and Connie Page ............. v Contributors to this volume ................................................. vii PROBABILITY, BAYESIAN INFERENCE AND STOCHASTIC PROCESS Group invariant inferred distributions via noncommutative probability B. Heller and M. Wang ................................... 1 Invariance principles for fractionally integrated nonlinear processes Wei Biao Wu and Xiaofeng Shao .............................
  • IMS Bulletin

    IMS Bulletin

    Volume 36 • Issue 3 IMS Bulletin April 2007 IMS launches two new journals Statistics Surveys CONTENTS Statistics Surveys is a new open access, electronic journal, sponsored by IMS and the 1 New IMS journals Bernoulli Society. Statistics Surveys publishes survey articles in theoretical, applied, and computational statistics. The style of articles may range from reviews of recent 2–3 IMS Members’ News: Michael Woodroofe, Arak research to graduate textbook exposition. Articles may be broad or narrow in scope. Mathai, Howell Tong The essential requirements are a well-specified topic and target audience, together with clear exposition. 4 Board on Mathematical Jon Wellner Sciences & Applications We are pleased to announce the appointment of , University of Washington, as IMS Executive Editor, and Wendy L. Martinez, US Office of Naval 5 C R Rao Advanced Institute Research, as Coordinating Editor. 7 Profile: Bruno de Finetti Sponsorship from other societies is welcomed. Each sponsoring society appoints its own Executive Editor, who in turn has authority to appoint any number of Associate 8 NSF Statistics Program; Funding for Probability Editors on behalf of their sponsoring society (Associate Editors are sponsored by only one society). An initial set of twenty IMS-sponsored Associate Editors have been IMS Childcare Initiative; 10 appointed; for a listing see http://www.i-journals.org/ss/editors.php. To discuss the NSF-CBMS Conferences potential involvement of a new sponsoring society, please contact Wendy 11 Terence’s Stuff: Model Martinez at [email protected]. Skeptics The journal can be accessed at http://www.i-journals.org/ss/. 12 IMS Meetings You can sign up to receive an email notification of each new issue’s Table of Contents — this also indicates your support, to 17 Other Meetings and Announcements editors and sponsors, for the journal’s work.