Annals of Statistics

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

Nicolas Privault and Anthony Réveillac

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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].

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Ann. Statist., Volume 36, Number 5 (2008), 2531-2550.

First available in Project Euclid: 13 October 2008

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Zentralblatt MATH identifier

Primary: 62G05: Estimation 60H07: Stochastic calculus of variations and the Malliavin calculus 31B05: Harmonic, subharmonic, superharmonic functions

Nonparametric drift estimation Stein estimation Gaussian space Malliavin calculus harmonic analysis


Privault, Nicolas; Réveillac, Anthony. Stein estimation for the drift of Gaussian processes using the Malliavin calculus. Ann. Statist. 36 (2008), no. 5, 2531--2550. doi:10.1214/07-AOS540.

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