This book provides a self-contained, linear, and unified introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. The targeted audience includes statisticians, biostatisticians, and other researchers with a background in mathematical statistics who have an interest in learning about and doing research in empirical processes and semiparametric inference but who would like to have a friendly and gradual introduction to the area. The book can be used either as a research reference or as a textbook. The level of the book is suitable for a second year graduate course in statistics or biostatistics, provided the students have had a year of graduate level mathematical statistics and a semester of probability. The book consists of three parts. The first part is a concise overview of all of the main concepts covered in the book with a minimum of technicalities. The second and third parts cover the two respective main topics of empirical processes and semiparametric inference in depth. The connections between these two topics is also demonstrated and emphasized throughout the text. Each part has a final chapter with several case studies that use concrete examples to illustrate the concepts developed so far. The last two parts also each include a chapter which covers the needed mathematical preliminaries. Each main idea is introduced with a non-technical motivation, and examples are given throughout to illustrate important concepts. Homework problems are also included at the end of each chapter to help thereader gain additional insights.
I Overview 1
1 Introduction 3
2 An Overview of Empirical Processes 9
3 Overview of Semiparametric Inference 35
4 Case Studies I 49
II Empirical Processes 75
5 Introduction to Empirical Processes 77
6 Preliminaries for Empirical Processes 81
7 Stochastic Convergence 103
8 Empirical Process Methods 127
9 Entropy Calculations 155
10 Bootstrapping Empirical Processes 179
11 Additional Empirical Process Results 207
12 The Functional Delta Method 235
13 Z-Estimators 251
14 M-Estimators 263
15 Case Studies II 283
III Semiparametric Inference 317
16 Introduction to Semiparametric Inference 319
17 Preliminaries for Semiparametric Inference 323
18 Semiparametric Models and Efficiency 333
19 Efficient Inference for Finite-Dimensional Parameters 349
20 Efficient Inference for Infinite-Dimensional Parameters 379
21 Semiparametric M-Estimation 397
22 Case Studies III 425
References 459
Author Index
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