This book provides an account of weak convergence theory and empirical processes and their applications to a wide variety of applications in statistics. The first part of the book presents a thorough account of stocastic 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 topics which demonstrate the applicability of the theory to important questions such limit theorems in asymptotic statistics; measures of goodness of fit; the bootstrap; and semiparametric estimation. Most of the sections conclude with and “problems and complements and “. Some of these are exercises to help the reader’s understanding of the material whereas others are intended to supplement the text.

Weak Convergence and Empirical Processes: With Applications to Statistics (Springer Series in Statistics) by A.W. van der vaart (2000-11-10) PDF

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