STEIN ESTIMATION FOR THE DRIFT OF GAUSSIAN PROCESSES USING THE MALLIAVIN CALCULUS
成果类型：
Article
署名作者：
Privault, Nicolas; Reveillac, Anthony
署名单位：
City University of Hong Kong; La Rochelle Universite
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/07-AOS540
发表日期：
2008
页码：
2531-2550
关键词：
摘要：
We consider the nonparametric functional estimation of the drift of a Gaussian process via minimax and Bayes estimators. In this context, we construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and superharmonic functionals on Gaussian space. Our results are illustrated by numerical simulations and extend the construction of James-Stein type estimators for Gaussian processes by Berger and Wolpert [J. Multivariate Anal. 13 (1983) 401-424].