Introduction to Empirical Processes and Semiparametric Inference

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Springer, Dec 29, 2007 - Mathematics - 483 pages
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The goal of this book is to introduce statisticians, and other researchers with a background in mathematical statistics, to empirical processes and semiparametric inference. These powerful research techniques are surpr- ingly useful for studying large sample properties of statistical estimates from realistically complex models as well as for developing new and - proved approaches to statistical inference. This book is more of a textbook than a research monograph, although a number of new results are presented. The level of the book is more - troductory than the seminal work of van der Vaart and Wellner (1996). In fact, another purpose of this work is to help readers prepare for the mathematically advanced van der Vaart and Wellner text, as well as for the semiparametric inference work of Bickel, Klaassen, Ritov and We- ner (1997). These two books, along with Pollard (1990) and Chapters 19 and 25 of van der Vaart (1998), formulate a very complete and successful elucidation of modern empirical process methods. The present book owes much by the way of inspiration, concept, and notation to these previous works.What is perhaps new is the gradual—yetrigorous—anduni?ed way this book introduces the reader to the ?eld.
 

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Contents

Introduction
3
Overview of Semiparametric Inference 35
34
Case Studies I
49
Empirical Processes
75
Stochastic Convergence
103
Empirical Process Methods
127
Entropy Calculations 155
154
Bootstrapping Empirical Processes
179
Case Studies II
283
Introduction to Semiparametric Inference
319
Semiparametric Models and Efficiency
333
Efficient Inference for FiniteDimensional Parameters
349
Efficient Inference for InfiniteDimensional Parameters 379
378
Semiparametric MEstimation
397
Case Studies III
424
References
459

Additional Empirical Process Results
207
The Functional Delta Method 235
234
ZEstimators
251
Author Index
470
Subject Index
477
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