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

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.