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Weak Convergence and Empirical Processes

Name: Weak Convergence and Empirical Processes
Brand: Springer Nature B.V.
SKU: 50452354
Price: 231.81 PLN
Availability: InStock
Author: A. W. van der Vaart
ISBN: 9783031290398

With Applications to Statistics

A. W. van der Vaart

Jon A. Wellner

Język

Angielski

Książka Miękka

Kod Libristo: 50452354

Wydawnictwo Springer Nature B.V., lipiec 2023

This book provides an account of weak convergence theory, empirical processes, and their application... Cały opis

Kod Libristo: 50452354

131 b

231.81 zł

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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.