Empirical Processes in M-Estimation

Sara A. van de Geer (Rijksuniversiteit Leiden, The Netherlands)

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English

Cambridge University Press
19 November 2009

Mathematics & Sciences; Probability & statistics

Series: Cambridge Series in Statistical and Probabilistic Mathematics

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.

By: Sara A. van de Geer (Rijksuniversiteit Leiden The Netherlands)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 6
Dimensions: Height: 254mm, Width: 178mm, Spine: 16mm
Weight: 530g
ISBN: 9780521123259
ISBN 10: 0521123259
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Pages: 300
Publication Date: 19 November 2009
Audience: Professional and scholarly , Professional and scholarly , Undergraduate , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Empirical Processes in M-Estimation

'... 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