Nonparametric Estimation of the Fractional Derivative of a Distribution Function
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.
|Date of creation:||2010|
|Date of revision:|
|Note:||View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00536979/en/|
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