Cramèr-Rao bounds for fractional Brownian motions

Jean-François Coeurjolly (1) , Jacques Istas (1)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul

We obtain Cramèr–Rao bounds for parameters estimators of fractional Brownian motions. We point out the differences of behavior whether these processes are standard or not. The key-point of this study relies upon a linear algebra result we prove, exhibiting bounds for elements of inverse of localized matrices.

Mots clés: Cramèr–Rao bounds; Fractional Brownian motion; Invertibility of localized matrices

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-François Coeurjolly, Jacques Istas. Cramèr-Rao bounds for fractional Brownian motions. Statistics and Probability Letters, 2001, 53 (4), pp.435--447. ⟨10.1016/S0167-7152(00)00197-8⟩. ⟨hal-00383117⟩