Nonparametric Estimation of the Fractional Derivative of a Distribution Function

Andreea Borla (1) , Costin Protopopescu (1)

1 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

We propose an estimator for the fractional derivative of a distribution function. Our estimator, based on finite differences of the empirical distribution function generalizes the estimator proposed by Maltz for the nonnegative real case. The asymptotic bias, variance and the consistency of the estimator are studied. Finally, the optimal choice for the ''smoothing parameter'' proves that even in the fractional case, the Stone's rate of convergence is achieved.

Mots clés: fractional derivative; nonparametric estimation; distribution function; generalized differences

Domaines: Economies et finances

Andreea Borla, Costin Protopopescu. Nonparametric Estimation of the Fractional Derivative of a Distribution Function. 2010. ⟨halshs-00536979⟩