A New Smooth Density Estimator for Non-Negative Random Variables

Abstract

Commonly used kernel density estimators may not provide admissible values of the density or its functionals at the boundaries for densities with restricted support. For smoothing the empirical distribution a generalization of the Hille's lemma, considered here, alleviates some of the problems of kernel density estimator near the boundaries. For nonnegative random variables which crop up in reliability and survival analysis, the proposed procedure is thoroughly explored; its consistency and asymptotic distributional results are established under appropriate regularity assumptions. Methods of obtaining smoothing parameters through cross-validation are given, and graphical illustrations of the estimator for continuous (at zero) as well as discontinuous densities are provided