Introduction to Empirical Processes and Semiparametric Inference

1. Front Matter

   Pages i-xiv

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2. Overview

   1. Introduction

      Pages 3-7

   2. An Overview of Empirical Processes

      Pages 9-33

   3. Overview of Semiparametric Inference

      Pages 35-48

   4. Case Studies I

      Pages 49-73

3. Empirical Processes

   1. Introduction to Empirical Processes

      Pages 77-79

   2. Preliminaries for Empirical Processes

      Pages 81-102

   3. Stochastic Convergence

      Pages 103-126

   4. Empirical Process Methods

      Pages 127-153

   5. Entropy Calculations

      Pages 155-178

   6. Bootstrapping Empirical Processes

      Pages 179-205

   7. Additional Empirical Process Results

      Pages 207-233

   8. The Functional Delta Method

      Pages 235-250

   9. Z-Estimators

      Pages 251-262

   10. M-Estimators

       Pages 263-282

   11. Case Studies II

       Pages 283-316

4. Semiparametric Inference

   1. Introduction to Semiparametric Inference

      Pages 319-321

   2. Preliminaries for Semiparametric Inference

      Pages 323-332

   3. Semiparametric Models and Efficiency

      Pages 333-347

   4. Efficient Inference for Finite-Dimensional Parameters

      Pages 349-377

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.

• Asymptotic statistics
• Bootstrap theory
• Bootstrapping
• Distribution theory
• Empirical Process
• Estimator
• Statistical efficiency
• mathematical statistics

From the reviews:

"Introduction to Empirical Processes and Semiparametric Inference is a very good combination of both the empirical processes and semiparametric theories. This is the first book of its kind....I agree with the author that this book is 'more of a textbook than a research monograph.' As the semiparametric inference is currently an extremely active research area in statistical research, the book will open the door for graduate students to identify significant future research potentials. In fact, this book contains the author's newest research result, the application of semiparametric method in microarray data analysis. This book can be used as a textbook for graduate students in statistics, biostatistics, and economics (econometrics). In fact, the contents of this book can be tailored for different courses."

"Generally, this is a great book on empirical processes and semiparametric methods. It should be on the must-read list for a serious statistician, biostatistician, or econometrician." (Biometrics, September 2008)

"The main focus of this book is to introduce empirical processes and semiparametric inference methods to researchers interested in developing inferential tools for relatively complicated mathematical or statistical modeling problems. ...The material is structured in a sensible way supporting the learning and understanding of useful and challenging techniques of empirical processes and semiparametric inference. The book could well be very helpful for those studying and applying these techniques." (International Statistical Review 2008,77,2)

“This book is an introduction to what is commonly called the modern theory of empirical processes – empirical processes indexed by classes of functions – and to semiparametric inference, and the interplay between both fields. … This is clearly intended to be a book for the novice in empirical process theory and semiparametricinference. … The main material is presented in a clearly arranged and logical order. … will be useful to anybody who wants to learn about the modern theory of empirical processes and semiparametric inference.” (Erich Häusler, Zentralblatt MATH, Vol. 1180, 2010)

• Department of Biostatistics, University of North Carolina, Chapel Hill, USA

  Michael R. Kosorok

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