A comparison of Several Bandwidth Selection Methods for Local Polynomial Regression

Abstract

 In local polynomial regression, choosing the smoothing parameter (bandwidth) is a crucial issue. A too large value provide over smoothing. Conversely, a too small value gives a wiggly estimate which result in under smoothing. However, the proper choice of bandwidth can be considered as a careful balance of these principles. In this paper, intensive simulation experiments are carried out using R software to compare the practical performance of several bandwidth selection methods, namely the Cross Validation (CV), Generalized Cross Validation (GCV), and Adaptive (ADP).Within the context of these strategies of selecting the optimal bandwidth(s), four different example-regression models have been used under different sample sizes and kernel functions. Results showed that the (GCV) bandwidth selection criterion appears to give better (smaller) estimates of MSE when the sample  sizes (n) are small; with Gaussian kernel function. However, the (Adp) bandwidth selection appears to give better (smaller) estimates of MSE when the sample sizes (n) are large with Triweight l kernel function.