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

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

2008-11-07

arxiv.org/abs/0811.1153v1

Annals of Statistics 2008, Vol. 36, No. 5, 2531-2550

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS540 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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