Estimation of the drift of fractional Brownian motion

Abstract

We consider the problem of efficient estimation for the drift of fractional Brownian motion $B^H:=(B_t^H{)}_{t\in [0,T]}$ 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.