BIAS CORRECTION AT END POINTS IN KERNEL DENSITY ESTIMATION

Abstract

In this thesis, we study some boundary correction methods for kernel estimators of the density function and their statistical properties. The kernel estimators are not consistent near the finite end points of their supports. In other words, these effects seriously affect the performance of these estimators. To remove these boundary effects, various methods have been developed in the literature, the most used are the reflection method, the transformation and the local linear methods. We combine transformation and reflection methods in order to introduce a new boundary correction estimator in the case of kernel estimation of the density function whose support is [0,1].