CHOICE OF BANDWIDTH IN KERNEL DENSITY ESTIMATION

ABSTRACT 

The kernel density estimator is a widely used tool in nonparametric density estimator. Choice of kernel function and bandwidth selection is two important issues on implementing kernel density estimation. However, the main drawback of the kernel density estimator happens when the underlying density has long tails. In this case, if the bandwidth is small, spurious noise appears in the tail of the estimates. Important features of the main part in the distribution may be lost due to the over smoothing. To avoid this problem, adaptive bandwidth selection methods should be used or put in place where the size if the bandwidth depends in the location of the estimator. The choice of bandwidth is very relevant in nonparametric density estimation and some of the proposed method for selecting the smoothing parameter h such as the plug in methods, cross validation method, rule of thumb method, et al has been reviewed. The problem of selecting the smoothing parameter h for a kernel estimator and also the purpose of estimation are the major drawbacks of bandwidth selection and the effectiveness of kernel density estimations is linked to the choice of bandwidth depending on an observed data. To this effect, we would be concentrating on the area; “Choice of bandwidth selection in kernel density estimation” because it’s a measure of how closely you want the density to match the distribution and its of great importance to density estimation. The choice of bandwidth selection is not only crucial to the kernel density estimation (KDE) but also crucial to the kernel based regressors.