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

Research output: Contribution to journalArticle

14 Citations (Scopus)

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
Externally publishedYes

Fingerprint

Nonparametric Maximum Likelihood Estimation
White Noise Model
M-estimation
Maximal Inequality
Point Estimation
M-estimator
Empirical Process
Gaussian Model
Gaussian White Noise
Martingale
Jump
Rate of Convergence
Sufficient Conditions
Context
Empirical process
Maximum likelihood estimation
Rate of convergence

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

A maximal inequality for continuous martingales and M-estimation in a Gaussian white noise model. / Nishiyama, Yoichi.

In: Annals of Statistics, Vol. 27, No. 2, 04.1999, p. 675-696.

Research output: Contribution to journalArticle

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