Estimation of the drift of fractional Brownian motion

摘要

We consider the problem of efficient estimation for the drift of fractional Brownian motion B-H := (B-t(H))(t is an element of[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.