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Nonparametric Estimation of the Fractional Derivative of a Distribution Function

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  • Andreea Borla

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Costin Protopopescu

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

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.

Suggested Citation

  • Andreea Borla & Costin Protopopescu, 2010. "Nonparametric Estimation of the Fractional Derivative of a Distribution Function," Working Papers halshs-00536979, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00536979
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00536979
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    Keywords

    fractional derivative; nonparametric estimation; distribution function; generalized differences;
    All these keywords.

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