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.
- Maximum likelihood
- Rate of convergence
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty