On performance of multivariate product kernel density estimation consistency

Abstract

This paper examines the consistency that surrounds the Multivariate Quiweight product kernel function in achieving a better curve estimate and the target density. In revealing its features in the area of Multivariate Kernel Density Estimation of data, we adopted the Multivariate KDE product estimator to ascertain its generalized consistency expressions. This was done via the Taylor series expansion for all its higher order forms of dimensions. The expressions that were established are subject to real life data simulations of different sample sizes based on the dimensions that emanated from the Multivariate Quiweight product kernel functions; the data analysis showed that it has a smaller bias and variance which influences its global performance as the Multivariate Quiweight product kernel function order and m dimensions increase.