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

Nicolas Privault (1) , Anthony Réveillac (2)

1 SPMS-PAP-02-01 - Division of Physics and Applied Physics [Nanyang Technological University]
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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].

Mots clés: Nonparametric drift estimation; Stein estimation; Gaussian space; Malliavin calculus; harmonic analysis

Domaines: Probabilités [math.PR]

Nicolas Privault, Anthony Réveillac. Stein estimation for the drift of Gaussian processes using the Malliavin calculus. Annals of Statistics, 2008, 36 (05), pp.2531-2550. ⟨10.1214/07-AOS540⟩. ⟨hal-00918464⟩