Estimation of the drift of fractional Brownian motion

Khalifa Es-Sebaiy (1, 2, 3) , Idir Ouassou (1) , Youssef Ouknine (1)

1 UCA - Université Cadi Ayyad [Marrakech]
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 CES - Centre d'économie de la Sorbonne

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

Keywords: Fractional Brownian Motion; Stein estimate; MLE

Domains: Mathematics [math]; Probability [math.PR]; Mathematics [math]; Statistics [math.ST]; Statistics [stat]; Statistics Theory [stat.TH]

Khalifa Es-Sebaiy, Idir Ouassou, Youssef Ouknine. Estimation of the drift of fractional Brownian motion. Statistics and Probability Letters, 2009, 79 (14), pp.1647-1653. ⟨10.1016/j.spl.2009.04.004⟩. ⟨hal-00382581⟩