Empirical Processes in M-Estimation

Sara A. van de Geer

ISBN 10: 0521123259 / ISBN 13: 9780521123259

Published by Cambridge University Press, GB, 2009

The theory of empirical processes provides valuable tools for the development of asymptotic theory in (nonparametric) statistical models, and makes possible the unified treatment of a number of them. This book reveals the relation between the asymptotic behaviour of M-estimators and the complexity of parameter space. Virtually all results are proved using only elementary ideas developed within the book; there is minimal recourse to abstract theoretical results. To make the results concrete, a detailed treatment is presented for two important examples of M-estimation, namely maximum likelihood and least squares. The theory also covers estimation methods using penalties and sieves. Many illustrative examples are given, including the Grenander estimator, estimation of functions of bounded variation, smoothing splines, partially linear models, mixture models and image analysis. Graduate students and professionals in statistics as well as those with an interest in applications, to such areas as econometrics, medical statistics, etc., will welcome this treatment. Seller Inventory # LU-9780521123259

Synopsis:

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.

Review: '... 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

Bibliographic Details

Title: Empirical Processes in M-Estimation
Publisher: Cambridge University Press, GB
Publication Date: 2009
Binding: Paperback
Condition: New
Edition: Illustrated.