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October 2008 Stein estimation for the drift of Gaussian processes using the Malliavin calculus
Nicolas Privault, Anthony Réveillac
Ann. Statist. 36(5): 2531-2550 (October 2008). DOI: 10.1214/07-AOS540


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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Nicolas Privault. Anthony Réveillac. "Stein estimation for the drift of Gaussian processes using the Malliavin calculus." Ann. Statist. 36 (5) 2531 - 2550, October 2008.


Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1274.62256
MathSciNet: MR2458197
Digital Object Identifier: 10.1214/07-AOS540

Primary: 31B05 , 60H07 , 62G05

Keywords: Gaussian space , harmonic analysis , Malliavin calculus , Nonparametric drift estimation , Stein estimation

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 5 • October 2008
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