Gamma kernel estimation of multivariate density and its derivative on the nonnegative semi-axis by dependent data

2014/10/09 by L. A. Markovich, Markovich, L. A.
Engineering · Mathematics · #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1410.2507

openalex publication_date 2014/10/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on [0,∞). To this end we use the class of kernel estimators with asymmetric gamma kernel functions. The gamma kernels are nonnegative. They change their shape depending on the position on the semi-axis and are robust to the boundary bias problem. We investigate the mean integrated squared error (MISE) assuming dependent data with strong mixing and find the optimal bandwidth of the kernel as a minimum of the MISE. We derive the bias, the variance and the covariance of the density and of its partial derivative.

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