On a Generalization of a Smooth Estimator of Survival and Density Function
by
Yogendra P. Chaubey
Concordia University
Coauthors: Arusharka Sen and Pranab K. Sen

This paper considers a smooth version of the empirical distribution function for proposing a new non-parametric estimator of the probability density function that is motivated by the estimator considered in Chaubey and Sen (Statistics and Decisions, 1996) for densities with positive support. The resulting estimator is shown to be similar to the popular kernel estimator with the kernel having non-negative support. The case of gamma kernel is highlighted showing the contrast with the original proposal of Chaubey and Sen (1996) using discrete weights generated by an appropriate Poisson density. It is shown that under some regularity conditions, the proposed estimator is strongly consistent and asymptotically normally distributed.

Date received: August 27, 2003