We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the second-order terms in asymptotic expansion for the risk account for the behavior of the “nonparametric component” of a semiparametric procedure, and they are not dramatically smaller than the first-order terms.
Publié le : 2006-02-14
Classification:
Semiparametric estimation,
estimating a shift of a nonparametric function,
second-order efficiency,
penalized maximum likelihood,
exact minimax asymptotics,
62G05,
62G20
@article{1146576260,
author = {Dalalyan, A. S. and Golubev, G. K. and Tsybakov, A. B.},
title = {Penalized maximum likelihood and semiparametric second-order efficiency},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 169-201},
language = {en},
url = {http://dml.mathdoc.fr/item/1146576260}
}
Dalalyan, A. S.; Golubev, G. K.; Tsybakov, A. B. Penalized maximum likelihood and semiparametric second-order efficiency. Ann. Statist., Tome 34 (2006) no. 1, pp. 169-201. http://gdmltest.u-ga.fr/item/1146576260/