03475nam 22005535 450 991073485890332120250505001235.03-031-29040-210.1007/978-3-031-29040-4(MiAaPQ)EBC30627428(Au-PeEL)EBL30627428(DE-He213)978-3-031-29040-4(CKB)27561672700041(EXLCZ)992756167270004120230711d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierWeak Convergence and Empirical Processes With Applications to Statistics /by A. W. van der Vaart, Jon A. Wellner2nd ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (693 pages)Springer Series in Statistics,2197-568XPrint version: van der Vaart, A W Weak Convergence and Empirical Processes Cham : Springer International Publishing AG,c2023 9783031290381 Preface -- Reading Guide -- Part I: Stochastic Convergence -- Part 2: Empirical Processes -- Part 3: Statistical Applications -- Appendix -- References -- Author Index -- Subject Index -- List of Symbols.This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The first part of the book presents a thorough treatment of stochastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of applications in statistics including rates of convergence of estimators; limit theorems for M− and Z−estimators; the bootstrap; the functional delta-method and semiparametric estimation. Most of the chapters conclude with “problems and complements.” Some of these are exercises to help the reader’s understanding of the material, whereas others are intended to supplement the text. This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations ofsuprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.Springer Series in Statistics,2197-568XStatisticsStatisticsApplied StatisticsStatistical Theory and MethodsBayesian InferenceStatistics.Statistics.Applied Statistics.Statistical Theory and Methods.Bayesian Inference.519van der Vaart A W1372688Wellner Jon A613554MiAaPQMiAaPQMiAaPQBOOK9910734858903321Weak Convergence and Empirical Processes3403567UNINA