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

Yoichi Nishiyama

doi:10.1214/aos/1018031212

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

Yoichi Nishiyama^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 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 language	English
Pages (from-to)	675-696
Number of pages	22
Journal	Annals of Statistics
Volume	27
Issue number	2
DOIs	https://doi.org/10.1214/aos/1018031212
Publication status	Published - 1999 Apr
Externally published	Yes

Keywords

Martingale
Maximum likelihood
Rate of convergence
Regression
Sieve

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/aos/1018031212

Cite this

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AB - 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.

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KW - Maximum likelihood

KW - Rate of convergence

KW - Regression

KW - Sieve

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

Abstract

Keywords

ASJC Scopus subject areas

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