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Look Inside Empirical Processes in M-Estimation

Empirical Processes in M-Estimation

$54.99 (C)

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: November 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521123259

$ 54.99 (C)

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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 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.

    • 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: November 2009
    • 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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