Empirical Processes in M-Estimation (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 6) - Hardcover

Van De Geer, Sara A.

Hardcover

ISBN 10: 052165002X ISBN 13: 9780521650021

Publisher: Cambridge University Press, 2000

Synopsis

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.

About this title

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

Book Description

This book deals with estimation methods in statistics, and treats various models in a unified way. Many illustrative examples are given, including the Grenander estimator, smoothing splines, partially linear models, mixture models and image analysis. Graduate students and professionals in statistics will welcome this treatment.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2000
• Language: English
• ISBN 10: 052165002X
• ISBN 13: 9780521650021
• Binding: Hardcover
• Number of pages: 298