Parameter Estimation Based on Cumulative Kullback–Leibler Divergence

Abstract

In this paper, we propose some estimators for the parameters of a statistical model based on Kullback–Leibler divergence of the survival function in continuous setting and apply it to type I censored data. We prove that the proposed estimators are subclass of “generalized estimating equations” estimators. The asymptotic properties of the estimators such as consistency and asymptotic normality are investigated. Some illustrative examples are also provided. In particular, in estimating the shape parameter of generalized Pareto distribution, we show that our procedure dominates some existing methods in the sense of bias and mean squared error.