A maximal inequality for continuous martingales and M-estimation in a Gaussian white noise model

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Abstract

Some sufficient conditions to establish the rate of convergence of certain M-estimators in a Gaussian white noise model are presented. They are applied to some concrete problems, including jump point estimation and nonparametric maximum likelihood estimation, for the regres-sion function. The results are shown by means of a maximal inequality for continuous martingales and some techniques developed recently in the context of empirical processes.

Original languageEnglish
Pages (from-to)675-696
Number of pages22
JournalAnnals of Statistics
Volume27
Issue number2
Publication statusPublished - 1999 Apr 1

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Keywords

  • Martingale
  • Maximum likelihood
  • Rate of convergence
  • Regression
  • Sieve

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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