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. 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.

中文翻译：

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密度比模型下两个半连续种群基尼指数的半参数推断

基尼指数是一种流行的不平等衡量指标，在社会和经济研究中有许多应用。本文研究了两个半连续种群的基尼系数的半参数推断。我们通过零处的离散点质量和连续偏斜正分量的混合来表征每个半连续总体的分布。然后采用半参数密度比模型来链接两个分布的正分量。我们提出了两个基尼指数的最大经验似然估计及其差异，并进一步研究了所提出估计的渐近特性。渐近结果使我们能够构建置信区间并对两个基尼指数及其差异进行假设检验。所提出的方法也适用于没有过多零值的情况。我们提出的方法优于一些现有方法的优越性在理论上和数值上都得到了证明。提供了两个真实数据应用程序以供说明。