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Author Privault, Nicolas ♦ Reveillac, Anthony
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-05-14
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics ♦ Probabilities & applied mathematics
Subject Keyword Mathematics - Statistics Theory ♦ Mathematics - Probability ♦ 62G05 ♦ 31B05 ♦ 60H07 ♦ math ♦ stat
Abstract In this paper we consider the nonparametric functional estimation of the drift of Gaussian processes using Paley-Wiener and Karhunen-Lo\`eve 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.
Educational Use Research
Learning Resource Type Article


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