Stein estimation for the drift of Gaussian processes using the Malliavin calculus
Statistics Theory
2018-08-18 v1 Statistics Theory
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].
Keywords
Cite
@article{arxiv.0811.1153,
title = {Stein estimation for the drift of Gaussian processes using the Malliavin calculus},
author = {Nicolas Privault and Anthony Réveillac},
journal= {arXiv preprint arXiv:0811.1153},
year = {2018}
}
Comments
arXiv admin note: substantial text overlap with arXiv:0805.2002