Introduction to Empirical Processes and Semiparametric Inference / by Michael R. Kosorok.

Format:

Book

Author/Creator:

Kosorok, Michael R.

Series:

Springer Series in Statistics, 2197-568X

Language:

English

Subjects (All):

Probabilities.

Statistics.

Probability Theory.

Statistical Theory and Methods.

Local Subjects:

Probability Theory.

Statistical Theory and Methods.

Physical Description:

1 online resource (495 p.)

Edition:

1st ed. 2008.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2008.

Language Note:

English

Summary:

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 the reader gain additional insights. Michael R. Kosorok is Professor and Chair, Department of Biostatistics, and Professor, Department of Statistics and Operations Research, at the University of North Carolina at Chapel Hill. His research has focused on the application of empirical processes and semiparametric inference to statistics and biostatistics. He is a Fellow of both the American Statistical Association and the Institute of Mathematical Statistics. He is an Associate Editor of the Annals of Statistics, Electronic Journal of Statistics, International Journal of Biostatistics, Statistics and Probability Letters, and Statistics Surveys.

Contents:

Overview

An Overview of Empirical Processes

Overview of Semiparametric Inference

Case Studies I

Empirical Processes

to Empirical Processes

Preliminaries for Empirical Processes

Stochastic Convergence

Empirical Process Methods

Entropy Calculations

Bootstrapping Empirical Processes

Additional Empirical Process Results

The Functional Delta Method

Z-Estimators

M-Estimators

Case Studies II

Semiparametric Inference

to Semiparametric Inference

Preliminaries for Semiparametric Inference

Semiparametric Models and Efficiency

Efficient Inference for Finite-Dimensional Parameters

Efficient Inference for Infinite-Dimensional Parameters

Semiparametric M-Estimation

Case Studies III.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [459]-469) and indexes.

ISBN:

1-281-21679-8

9786611216795

0-387-74978-0

OCLC:

233972325