Comparative Analysis of Density Estimation Based Kernel Regression

Abstract

The local linear kernel estimator (LLKE) is a typical kernel-type regression method which is a non-parametric method to estimate the conditional expectation of a random variable and the non-linear mapping from input to output. There are three commonly used LLKEs, i.e., the Nadaraya-Watson kernel estimator, the Priestley-Chao kernel estimator and the Gasser-Müller kernel estimator. Existing studies show that the performance of LLKE mainly depends on the selection of an important parameter, i.e. bandwidth $h$, when a special kernel function is employed. However, there is no comparative research conducted to study the effectiveness of different kernel functions. In this paper, we compare the performance of three aforementioned LLKEs based on 6 different kernel functions (i.e., Gaussian, uniform, Epanechnikov, biweight, triweight and cosine kernels) on their estimation error measured by the mean squared error (i.e., $mse$) and stability of method measured by the standard deviation of $mse$ (i.e., $std$). Finally, we give guidelines for the selection of LLKE method and corresponding kernel function in practical applications.