Empirical Processes in M-Estimation

by Sara A. van de Geer

Overview

The theory of empirical processes provides valuable tools for the development of asymptotic theory in (nonparametric) statistical models, and makes it possible to give a unified treatment of various models. This book reveals the relation between the asymptotic behavior of M-estimators and the complexity of parameter space, using entropy as a measure of complexity, presenting tools and methods to analyze nonparametric, and in some cases, semiparametric methods. Graduate students and professionals in statistics, as well as those interested in applications, e.g. to econometrics, medical statistics, etc., will welcome this treatment.

Product Details

ISBN-13:	9780521123259
Publisher:	Cambridge University Press
Publication date:	11/19/2009
Series:	Cambridge Series in Statistical and Probabilistic Mathematics , #6
Edition description:	Reissue
Pages:	300
Product dimensions:	7.00(w) x 10.00(h) x 0.70(d)

Table of Contents

Preface; Reading guide; 1. Introduction; 2. Notations and definitions; 3. Uniform laws of large numbers; 4. First applications: consistency; 5. Increments of empirical processes; 6. Central limit theorems; 7. Rates of convergence for maximum likelihood estimators; 8. The non-i.i.d. case; 9. Rates of convergence for least squares estimators; 10. Penalties and sieves; 11. Some applications to semi-parametric models; 12. M-estimators; Appendix; References; Author index; Subject index; List of symbols.

Editorial Reviews

'… well written and provides a modern contribution to a very important class of nonparametric estimators.' N. D. C. Veraverbeke, Publication of the International Statistical Institute

'… this excellent book will be extremely useful for graduate students and researchers in the general area of nonparametric estimation. It is a welcome addition to the existing literature and certainly recommended.' Niew Archief voor Wiskunde

From the Publisher