Comparative Analysis on Kernel Based Probability Density Estimation

Abstract

In this paper, we compare the estimation performances of 7 different kernels (i.e., Uniform, Triangular, Epanechnikov, Biweight, Triweight, Cosine and Gaussian) when using them to conduct the probability density estimation with Parzen window method. We firstly analyze the efficiencies of these 7 kernels and then compare their estimation errors measured by mean squared error (MSE). The theoretical analysis and the experimental comparisons show that the mostly-used Gaussian kernel is not the best choice for the probability density estimation, of which the efficiency is low and estimation error is high. The derived conclusions give some guidelines for the selection of kernel in the practical application of probability density estimation.