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The Gini index is a popular inequality measure with many applications in social and economic studies. This paper studies semiparametric inference on the Gini indices of two semicontinuous populations. We characterize the distribution of each semicontinuous population by a mixture of a discrete point mass at zero and a continuous skewed positive component. A semiparametric 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. We show that the proposed estimators are more efficient than the existing fully nonparametric estimators. The proposed estimators and the asymptotic results are also applicable to cases without excessive zero values. Simulation studies show the superiority of our proposed method over existing methods. Two real-data applications are presented using the proposed methods.
The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or additional
In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a discrete point ma
The Youden index is a popular summary statistic for receiver operating characteristic curve. It gives the optimal cutoff point of a biomarker to distinguish the diseased and healthy individuals. In this paper, we propose to model the distributions of
Simultaneous, post-hoc inference is desirable in large-scale hypotheses testing as it allows for exploration of data while deciding on criteria for proclaiming discoveries. It was recently proved that all admissible post-hoc inference methods for the
In mathematical finance, Levy processes are widely used for their ability to model both continuous variation and abrupt, discontinuous jumps. These jumps are practically relevant, so reliable inference on the feature that controls jump frequencies an