Semi-parametric inference on Gini indices of two semi-continuous populations under density ratio models

Abstract

Summary The Gini index is a popular inequality measure with many applications in social and economic studies. This paper studies semi-parametric inference on the Gini indices of two semi-continuous populations. We characterise the distribution of each semi-continuous population by a mixture of a discrete point mass at zero and a continuous skewed positive component. A semi-parametric density ratio model is then employed to link the positive components of the two distributions. We propose the maximum empirical likelihood estimators of the two Gini indices and their difference, and further investigate the asymptotic properties of the proposed estimators. The asymptotic results enable us to construct confidence intervals, and perform hypothesis tests for the two Gini indices and their difference. The proposed method is also applicable to cases without excessive zero values. The superiority of our proposed method over some existing methods is shown theoretically and numerically. Two real-data applications are presented for illustration.