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Stochastic analysis on Gaussian space applied to drift estimation

Réveillac, Anthony; Privault, Nicolas (2008), Stochastic analysis on Gaussian space applied to drift estimation. https://basepub.dauphine.fr/handle/123456789/7107

Type
Document de travail / Working paper
External document link
http://arxiv.org/abs/0805.2002v1
Date
2008
Publisher
Université de La Rochelle
Published in
La Rochelle
Pages
36
Metadata
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Author(s)
Réveillac, Anthony
Privault, Nicolas
Abstract (EN)
In this paper we consider the nonparametric functional estimation of the drift of Gaussian processes using Paley-Wiener and Karhunen-Loève expansions. We construct efficient estimators for the drift of such processes, and prove their minimaxity using Bayes estimators. We also construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and stochastic analysis on Gaussian space, in which superharmonic functionals of the process paths play a particular role. Our results are illustrated by numerical simulations and extend the construction of James-Stein type estimators for Gaussian processes by Berger and Wolper.
Subjects / Keywords
harmonic analysis; Malliavin calculus; Gaussian space; Stein estimation; Nonparametric drift estimation