Empirical Processes in M-Estimation (Relié)

Sara Van De Geer

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  • Cambridge University Press

  • Paru le : 02/03/2000
  • 1 million de livres à découvrir
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The theory of empirical processes provides valuable tools for the development of asymptotic theory in (non-parametric) statistical models, and possibly 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.
    • Notation and Definitions
    • Uniform Laws of Large Numbers
    • First Applications: Consistency
    • Increments of Empirical Processes
    • Central Limit Theorems
    • Rates of Convergence for Maximum Likelihood Estimators
    • The Non-IID Case
    • Rates of Convergence for Least Squares Estimators
    • Penalties and Sieves
    • Some Applications to Semiparametric Models
    • M-Estimators.

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Empirical Processes in M-Estimation
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