The Annals of Statistics

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

Nicolas Privault and Anthony Réveillac

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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].

Article information

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

Dates
First available in Project Euclid: 13 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1223908102

Digital Object Identifier
doi:10.1214/07-AOS540

Mathematical Reviews number (MathSciNet)
MR2458197

Zentralblatt MATH identifier
1274.62256

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1223908102


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References

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