广义Lorenz 曲线的非参数统计推断

本文讨论了广义Lorenz 曲线的经验似然统计推断. 在简单随机抽样、分层随机抽样和整群随机抽样下, 本文分别定义了广义Lorenz 坐标的pro le 经验似然比统计量, 得出这些经验似然比的极限分布为带系数的自由度为1 的χ² 分布. 对于整个Lorenz 曲线, 基于经验似然方法类似地得出相应的极限过程. 根据所得的经验似然理论, 本文给出了bootstrap 经验似然置信区间构造方法, 并通过数据模拟, 对新给出的广义Lorenz 坐标的bootstrap 经验似然置信区间与渐近正态置信区间以及bootstrap 置信区间等进行了对比研究. 对整个Lorenz 曲线, 基于经验似然方法对其置信域也进行了模拟研究. 最后我们将所推荐的置信区间应用到实例中.

Non-parametric inferences for the generalized Lorenz curve

In this paper, we discuss the empirical likelihood-based inferences for the generalized Lorenz （GL） curve. In the settings of simple random sampling, stratified random sampling and cluster random sampling, it is shown that the limiting distributions of the empirical likelihood ratio statistics for the GL ordinate are the scaled X2 distributions with one degree of freedom. We also derive the limiting processes of the associated empirical likelihood-based GL processes. Various confidence intervals for the GL ordinate are proposed based on bootstrap method and the newly developed empirical likelihood theory. Extensive simulation studies are conducted to compare the relative performances of various confidence intervals for GL ordinates in terms of coverage probability and average interval length. The finite sample performances of the empirical likelihood- based confidence bands are also illustrated in simulation studies. Finally, a real example is used to illustrate the application of the recommended intervals.