This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order asymptotic expansion of the risk of these estimators is obtained. Moreover, the minimax problem for the second-order term is studied and an estimator of the preceding class is shown to be second order efficient.
Publié le : 2007-11-14
Classification:
exact minimax asymptotics,
penalized maximum likelihood,
second-order efficiency,
semi-parametric estimation,
unknown period
@article{1194625595,
author = {Castillo, I.},
title = {Semi-parametric second-order efficient estimation of the period of a signal},
journal = {Bernoulli},
volume = {13},
number = {1},
year = {2007},
pages = { 910-932},
language = {en},
url = {http://dml.mathdoc.fr/item/1194625595}
}
Castillo, I. Semi-parametric second-order efficient estimation of the period of a signal. Bernoulli, Tome 13 (2007) no. 1, pp. 910-932. http://gdmltest.u-ga.fr/item/1194625595/