Maximum entropy and empirical likelihood in length-biased setting: a comparison study

Abstract

This paper focuses on comparing two nonparametric methods of constructing confidence intervals: the maximum entropy (ME) and the empirical likelihood (EL). The objective is to estimate probability distributions given some moment conditions in the presence of length-biased sampling. Some simulation studies are conducted to indicate ME confidence intervals have better coverage probabilities in comparison with their EL counter-parts, when the biased data are contaminated. At the end, the ME and EL methods are applied to analyze a set of real data on elderly residents of a retirement center.