Estimation of the drift of fractional Brownian motion

TL;DR

This paper addresses the challenge of estimating the drift of fractional Brownian motion with Hurst parameter less than 1/2, introducing efficient and superefficient estimators that outperform traditional methods.

Contribution

It develops new estimation techniques for fractional Brownian motion's drift, including James-Stein type estimators that are superefficient under quadratic risk.

Findings

Proposes efficient estimators for fractional Brownian motion drift.

Constructs James-Stein type estimators that dominate maximum likelihood estimators.

Demonstrates improved estimation performance under quadratic risk.

Abstract

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.