Numerical computation of efficiency of beta polynomial kernel using product approach

Abstract

The efficiency values of beta polynomial kernel functions were computed using bivariate product approach, which involved multiplication of two univariate beta kernel functions. The statistical properties of bivariate beta kernel functions, in terms of roughness and variance, were evaluated to compute the efficiency values. The efficiency values of univariate form of beta polynomial kernels were also determined, and compared with values of bivariate beta kernel functions, since most applications of kernel estimators are in the bivariate form. The kernel estimator is a non-parametric density estimator with direct applications in data analysis and visualization. The computations showed that efficiency values tended to be smaller for bivariate beta polynomial kernel functions than for univari-ate kernel functions, due to effects of dimensionality associated with non-parametric statistics.

Keywords: Bivariate Kernel, Kernel Estimator, Product Approach, Efficiency of Beta Polynomial