In this paper, we propose new semiparametric procedures for inference on linear functionals in the context of two semicontinuous populations. The distribution of each semicontinuous population is characterized by a mixture of a discrete point mass at zero and a continuous skewed positive component. To utilize the information from both populations, we model the positive components of the two mixture distributions via a semiparametric density ratio model. Under this model setup, we construct the maximum empirical likelihood estimators of the linear functionals. The asymptotic normality of the proposed estimators is established and is used to construct confidence regions and perform hypothesis tests for these functionals. We show that the proposed estimators are more efficient than the fully nonparametric ones. Simulation studies demonstrate the advantages of our method over existing methods. Two real-data examples are provided for illustration.

在本文中，我们提出了新的半参数程序，用于在两个半连续种群的背景下对线性泛函进行推理。每个半连续种群的分布特征是零点离散点质量和连续偏斜正分量的混合。为了利用来自两个种群的信息，我们通过半参数密度比模型对两个混合分布的正成分进行建模。在此模型设置下，我们构建线性泛函的最大经验似然估计量。建立了所提议估计量的渐近正态性，并用于构建置信区域和对这些泛函进行假设检验。我们表明，所提出的估计量比完全非参数的估计量更有效。模拟研究证明了我们的方法优于现有方法的优势。提供了两个真实数据示例进行说明。