Estimation of the drift of fractional Brownian motion

Es-Sebaiy Khalifa, Idir Ouassou, Youssef Ouknine

Published 2009-05-09Version 1

We consider the problem of efficient estimation for the drift of fractional Brownian motion $B^H:=(B^H_t)_{t\in[0,T]}$ with hurst parameter $H$ less than 1/2. We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.