General method of boundary correction in kernel regression estimation

Abstract

Kernel estimators of both density and regression functions are not consistent near the nite end points of their supports. In other words, boundary eects seriously aect the performance of these estimators. In this paper, we combine the transformation and the reflection methods in order to introduce a new general method of boundary correction when estimating the mean function. The asymptotic mean squared error of the proposed estimator is obtained. Simulations show that our method performes quite well with respect to some other existing methods.

Keywords: Boundary; Kernel estimation; Mean squared error; Regression; Estimation