Estimation of the drift of a Gaussian process under balanced loss function

Jabrane Moustaaid and Idir Ouassou

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 23, 8225-8245

Abstract: In this article, we study the problem of estimation of the drift θ of a Gaussian process (Xt)t∈[0,T]. We give a class of estimators of James-Stein type whose risk is lower than the risk of the maximum likelihood estimator (MLE) θ̂:=(Xt)t∈[0,T] under the balanced loss function. Moreover, in the multidimensional case we give a class of Baranchik-type estimators of the drift of a d-dimensional fractional Brownian motion whose risk is lower than the risk of the MLE under a weighted balanced loss function. Finally, we give a numerical simulations to illustrate our results.

Date: 2022
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DOI: 10.1080/03610926.2021.1890779

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