STEIN ESTIMATION FOR THE DRIFT OF GAUSSIAN PROCESSES
USING THE MALLIAVIN CALCULUS


Nicolas PRIVAULT

Poitiers University
France


ABSTRACT

Stein estimation for the drift of Gaussian processes using the Malliavin calculus. Abstract: We consider the nonparametric functional estimation of the drift of a Gaussian process via efficient 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 the Wiener space. Our results extend the construction of James-Stein type estimators for Gaussian processes by Berger and Wolpert (1983).



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