The weighted Hellinger distance in the multivariate kernel density estimation

Abstract

The kernel multivariate density estimation is an important technique to estimate the multivariate density function. In this investigation we will use Hellinger Distance as a measure of error to evaluate the estimator, we will derive the mean weighted Hellinger distance for the estimator, and we obtain the optimal bandwidth based on Hellinger distance. Also, we propose and study a new technique to select the matrix of bandwidths based on Hellinger distance, and compare the new technique with the plug-in and the least squares techniques.