A Comparative Study for Bandwidth Selection in Kernel Density Estimation

Abstract

Nonparametric kernel density estimation method makes no assumptions on the functional form of the curves of interest and hence allows flexible modeling of the data. Many authors pointed out that the crucial problem in kernel density estimation method is how to determine the bandwidth (smoothing) parameter. In this paper, we introduce the most important bandwidth selection methods. In particular, least squares cross-validation, biased cross-validation, direct plug-in, solve-the-equation rules and contrast methods are considered. These methods are described and their expressions are presented. Our main practical contribution is a comparative simulation study that aims to isolate the most promising methods. The performance of each method is evaluated on the basis of the mean integrated squared error and for small-to-moderate sample size. The simulation results showed that the contrast method is the most promising methods based on the simulated families that are considered.