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 regression 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.
Publié le : 1999-04-14
Classification:
Martingale,
rate of convergence,
regression,
maximum likelihood,
sieve,
62G05,
62F12,
60G15,
60G44
@article{1018031212,
author = {Nishiyama, Yoichi},
title = {A maximal inequality for continuous martingales and
$M$-estimation in a Gaussian white noise model},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 675-696},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031212}
}
Nishiyama, Yoichi. A maximal inequality for continuous martingales and
$M$-estimation in a Gaussian white noise model. Ann. Statist., Tome 27 (1999) no. 4, pp. 675-696. http://gdmltest.u-ga.fr/item/1018031212/