摘要
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profile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.
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.
出处
《中国科学：数学》
CSCD
北大核心
2012年第3期235-250,共16页
Scientia Sinica：Mathematica
基金
US National Security Agency(批准号:H98230-12-1-0228)资助项目
关键词
经验似然
广义
LORENZ曲线
置信区间
empirical likelihood, generalized Lorenz curve, confidence interval
