A Comparative Study for Bandwidth Selection in Kernel Density Estimation

Abstract

Nonparametric kernel density estimation method does not make any assumptions regarding the functional form of curves of interest; hence it allows flexible modeling of data. A crucial problem in kernel density estimation method is how to determine the bandwidth (smoothing) parameter. This article examines the most important bandwidth selection methods, in particular, least squares cross-validation, biased crossvalidation, direct plug-in, solve-the-equation rules and contrast methods. Methods are described and expressions are presented. The 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 for small-to-moderate sample size. Simulation results show that the contrast method is the most promising methods based on the simulated families considered.