A study on the efficiency of new beta polynomial kernels

Kernel density estimation is a widely used nonparametric method for estimating the probability density functions of observed data. The efficiency of the kernel method is significantly influenced by the choice of the kernel function and other statistical properties such as its roughness and variance. This study investigated the new beta polynomial family's efficiency and compared the efficiency values with the classic beta kernel family. The roughness and variance of the new core functions were determined to calculate the efficiency values. The numerical values of the efficiency of the classic beta family and the new family were determined and compared for univariate and bivariate kernel functions. The results of the study showed that the new beta family has higher efficiency values compared to the classic beta family. The higher efficiency of the proposed beta family is due to their coefficients being larger than the classic kernel functions.