Applications of empirical process theory

著者

書誌事項

Applications of empirical process theory

Sara A. van de Geer

（Cambridge series on statistical and probabilistic mathematics）

Cambridge University Press, 2009, c2000

  • : hbk
  • : pbk

タイトル別名

Empirical processes in M-estimation

大学図書館所蔵 件 / 全12件

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注記

"First published 2000. Reprinted 2006. This digitally printed version 2009."--T.p. verso

Includes bibliographical references (p. [272]-278) and indexes

内容説明・目次

内容説明

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.

目次

  • Preface
  • 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
  • Appendix
  • References
  • Author index
  • Subject index
  • List of symbols.

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