Kernel Function and Nonparametric Regression Estimation: Which Function is Appropriate?

Abstract

In regression estimation, researchers have the option of using parametric or nonparametric regression estimation. Because of the challenges that one can encounter as a result of model misspecification in the parametric type of regression, the nonparametric type of regression has become popular. This paper explores this type of regression estimation. Kernel estimation usually forms an integral part in this type of regression. There are a number of functions available for such a use. The goal of this study is to find out an appropriate function that can be used for weighting in regression estimation. Though from the theoretical results epanechnikov function is the optimal one, there are situations where Gaussian function may be advantageous. Simulations show that the estimates inherit the smoothness of the kernel functions used.