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

By Nicolas Privault, Anthony R'eveillac. 2008

34 citations recorded by the source corpus.

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].

Subfields: Finance, Statistics and Probability

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Citations in the corpus

Kernel Mean Estimation and Stein's Effect (2013, neutral): “Although some attempts have been made to understand this phenomenon in the infinite-dimensional space [17, 18, 19], this work presents a key challenge: the true probability distribution of μP is essentially unknown and is subject to the choice of kernel k and distribution P, whereas all the previous”
Exact maximum likelihood estimators for drift fractional Brownian motions (2009, background): “The parameter estimation problem for long memory processes have been wellstudied (see [1], [3], [4], [9], [11]).”
Stein’s method on Wiener chaos (2007, methodology): “The reader is referred to [42] for applications of integration by parts techniques to the Stein-type estimation of drifts of Gaussian processes.”