Nonparametric gamma kernel estimators of density derivatives on positive semiaxis

2014/01/27 by А. В. Добровидов, Dobrovidov, A. V., L. A. Markovich +1
Energy · Mathematics · #Coal and Coke Industries Research #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1401.6783

openalex publication_date 2014/01/27 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider nonparametric estimation of the derivative of a probability density function with the bounded support on [0,∞). Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma kernels is due to the fact they are nonnegative, change their shape depending on the position on the semi-axis and possess other good properties. We found analytical expressions for bias, variance, mean integrated squared error (MISE) of the derivative estimate. An optimal bandwidth, the optimal MISE, and rate of mean square convergence of the estimates for density derivative have also been found.

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