论文标题
对两个半连续种群的一般功能的半参数推断
Semiparametric inference on general functionals of two semicontinuous populations
论文作者
论文摘要
在本文中，我们提出了新的半参数程序，以推断两个半连续种群的线性功能及其功能。每个种群的分布通常以零以零和连续偏斜的阳性成分的混合物为特征，因此这种分布在性质上是半连续的。为了利用来自两个人群的信息，我们通过半参数密度比率模型对两个混合物分布的正分量进行建模。在此模型设置下，我们构建了线性函数及其功能的最大经验可能性估计量，并建立了提议的估计器的渐近正态性。我们显示，线性功能的估计值比完全非参数更有效。开发的渐近结果使我们能够构建置信区并为线性功能及其功能进行假设检验。我们进一步将这些结果应用于几个重要的摘要量，例如矩，平均比率，变异系数以及不平等措施的广义熵类。仿真研究证明了我们提出的半参数方法比某些现有方法的优势。提供了两个真实的数据示例供插图。
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 mass at zero and a continuous skewed positive component, and hence such distribution is semicontinuous in the nature. 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 and their functions, and establish the asymptotic normality of the proposed estimators. We show the proposed estimators of the linear functionals are more efficient than the fully nonparametric ones. The developed asymptotic results enable us to construct confidence regions and perform hypothesis tests for the linear functionals and their functions. We further apply these results to several important summary quantities such as the moments, the mean ratio, the coefficient of variation, and the generalized entropy class of inequality measures. Simulation studies demonstrate the advantages of our proposed semiparametric method over some existing methods. Two real data examples are provided for illustration.
