On improve boundary effect in kernel distribution estimation

Abstract

In this thesis, we propose a new estimator for improve boundary effects in kernel estimator of the heavy-tailed distribution function specially the Pareto-type distributions and its bias, variance and mean squared error are determined. Kernel methods are widely used in many research areas in statistics. However, kernel estimators suffer from boundary effects when the support of the function to be estimated has finite end points. Boundary effects seriously affect the overall performance of the estimator. To remove the boundary effects, a variety of methods have been developed in the literature, the most widely used is the reflection, the transformation ... In this thesis, we introduce a new method of boundary correction when estimating the heavy-tailed distribution function. Our technique is kind of a generalized reflection method involving reflecting a transformation of the observed data by modified Champernowne distribution function