Title: Multivariate generalised gamma kernel density estimators and application to non-negative data

Authors: Lynda Harfouche; Nabil Zougab; Smail Adjabi

Addresses: Research Unit LaMOS, University of Bejaia, Algeria ' Research Unit LaMOS, University of Bejaia, Algeria ' Research Unit LaMOS, University of Bejaia, Algeria

Abstract: This paper proposes a classical multivariate generalised gamma (GG) kernel estimator for probability density function (pdf) estimation in the context of multivariate nonnegative data. Then, we show that the multiplicative bias correction (MBC) techniques can be applied for multivariate GG kernel density estimator as in Funke and Kawka (2015). Some properties (bias, variance and mean integrated squared error) of the corresponding estimators are also provided. The choice of the vector of bandwidths is investigated by adopting the popular cross-validation technique. Finally, the performances of the classical and MBC estimator based on the family of GG kernels are illustrated by a simulation study and real data.

Keywords: asymmetric kernels; bandwidth; generalised gamma kernels; multiplicative bias correction; MBC; multivariate estimation density.

DOI: 10.1504/IJCSM.2020.106391

International Journal of Computing Science and Mathematics, 2020 Vol.11 No.2, pp.137 - 157

Received: 09 Aug 2017
Accepted: 02 Oct 2017

Published online: 31 Mar 2020 *

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