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Weak Convergence and Empirical Processes

With Applications to Statistics

A. W. Van Der Vaart, Jon A. Wellner


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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.

Détails
Auteur
A. W.  van der Vaart , Jon A.  Wellner
Marque
Springer
Collection
Springer Series in Statistics
Parution
2023-07-11
Pages
679 pages
EAN papier
9783031290381
Langue
Anglais
Informations ebook
EAN PDF
9783031290404
Prix
137,14 €
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Nb pages copiables 6
Nb pages imprimables 67
Taille du fichier 8776 Ko
Ce livre est accessible aux handicaps   Informations sur l'accessibilité
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Auteur(s) du livre


Defaut-Illustration A. W. van der Vaart
Defaut-Illustration Jon A. Wellner
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