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Look Inside Empirical Processes in M-Estimation

Empirical Processes in M-Estimation


Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: January 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521123259

£ 44.99

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About the Authors
  • 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.

    • Contains an introduction to empirical processes with a minimum of 'heavy' theory on weak convergence for non-measurable elements in abstract spaces
    • Presents a theory that can be directly applied
    • Provides proofs of virtually all results presented, using only elementary ideas but otherwise self-contained. Includes a large number of examples
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    Reviews & endorsements

    '… 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

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    Product details

    • Date Published: January 2010
    • format: Paperback
    • isbn: 9780521123259
    • length: 300 pages
    • dimensions: 254 x 178 x 16 mm
    • weight: 0.53kg
    • availability: Available
  • Table of Contents

    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
    Author index
    Subject index
    List of symbols.

  • Author

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

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