Jackknife empirical likelihood for comparing two Gini indices

Abstract

Abstract The focus of this paper is to derive the jackknife empirical likelihood for the difference of two Gini indices. For independent data we propose a novel U‐statistic, which allows direct utilization of the jackknife empirical likelihood without involving a nuisance parameter. For paired data we established Wilks’ theorem for the profile likelihood after maximization over the nuisance parameter. Simulation studies show that our method is comparable to existing empirical likelihood methods in terms of coverage accuracy, but obtains much shorter intervals. The proposed methods are illustrated via analyzing a real data set. The Canadian Journal of Statistics 44: 102–119; 2016 © 2016 Statistical Society of Canada