Stein estimation for the drift of Gaussian processes using the Malliavin calculus

Réveillac, Anthony; Privault, Nicolas

Réveillac, Anthony; Privault, Nicolas (2008), Stein estimation for the drift of Gaussian processes using the Malliavin calculus, Annals of Statistics, 36, 5, p. 2531-2550. http://dx.doi.org/10.1214/07-AOS540

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/0811.1153v1

Date

2008

Journal name

Annals of Statistics

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

2531-2550

Abstract (EN)

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].

Subjects / Keywords

Nonparametric drift estimation; Stein estimation; Gaussian space; Malliavin calculus; harmonic analysis