A New Second Order Kernel of the Beta Polynomial Family in Density Estimation

Abstract

Data exploratory analysis and data visualisations are the main functions of kernel density estimation. The kernel density estimation techniques depend fundamentally on the bandwidth that determines its smoothness and a kernel function. In this paper, a novel second order beta kernel from its classical counterpart with improved performance is introduced. The improvement of the newly introduced kernel family is ascribed to their possession of additional powers of derivatives since they are polynomial families. Although several techniques of kernel construction exist in literature, the proposed kernels were derived by modifying the additive higher order kernel construction rule. A real data and different sample sizes were employed in authenticating and validating the efficacy of the proposed kernels' performances using the asymptotic mean integrated squared error (AMISE) as the measure of accuracy. The results of the proposed kernels were compared with existing kernels with the proposed kernels outperforming the traditional kernels family.