Stein estimation for the drift of Gaussian processes using the Malliavin calculus
Nicolas Privault, Anthony Réveillac
The Annals of Statistics · 2008 · Volume 36 · Issue 5
Abstract
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].
Keywords
31B05, 60H07, 62G05, Gaussian space, harmonic analysis, Malliavin calculus, Nonparametric drift estimation, Stein estimation
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