Smoothing parameter values in automatic choice procedure and in acceptable interval in the kernel density estimation

Abstract

Automatic procedure for determining the parameters of kernel method, allows the simultaneous selection of two method parameters: kernel function and smoothing parameter. This approach simplifies the procedure for parameters selection and at the same time provides a good properties of kernel estimators. The second procedure regarded in the paper is the acceptable interval of values of smoothing parameter, allowing for a much more generalized approach in choosing the smoothing parameter in the kernel estimation. The results of the smoothing parameter values comparison, where these values are set in the automatic procedure and the procedure of the acceptable interval of smoothing parameters values in the estimation of density function, are presented in the paper. Comparison of these values is made basing on the results of applying the simulation methods. Basing on simulation studies results new intervals of values of smoothing parameter are proposed and analyzed.