Kernel estimation of the past entropy function with dependent data

Kernel estimation of past entropy function

Abstract

The past entropy function, introduced by Di Crescenzo and Longobardi
(2002), is viewed as a dynamic measure of uncertainty in past life. This measure find applications in modeling life time data. In the present work we provide non-parametric kernel type estimators for the past entropy function based on complete and censored data. Asymptotic properties of the estimators are established under suitable regularity conditions. Monte-Carlo simulation studies are carried out to compare the performance of the estimators using the meansquared error. The methods are illustrated using real data sets.