Asymptotic Results For Continuous Associated Kernel Estimators of Density Functions

Abstract

Symmetric kernel estimators of an unknown density function on a partial or totally bounded support suffer from edge effects and several authors considered specific asymmetric kernels, belonging in the large class of continuous associated kernels. Asymptotic properties of the corresponding estimators have been examined on a case-by-case basis. In this paper, it is proposed general asymptotic results for continuous associated kernel estimators; in particular, weak and strong global convergences are shown with respect to both uniform and $L^1$ norms. Three lognormal kernel estimators have used for illustrations and discussions. Finally, some concluding remarks are made.