纵向数据下部分线性EV模型中的经验似然  

Empirical likelihood for partially linear errors-in-variables models with longitudinal data

作　　者：谭晓燕 陈夏[1] 闫莉[1] TAN Xiaoyan;CHEN Xia;YAN Li(School of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《纺织高校基础科学学报》2018年第2期197-203,共7页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11201276);陕西省自然科学基础研究计划项目(2014JQ1042);全国统计科学研究项目一般项目(2017LY28);中央高校基本科研业务费专项资金项目(GK201503012)

摘　　要：为研究纵向数据部分线性EV模型参数的置信域问题,应用经验似然方法构造经验似然比统计量,证明了其极限分布为卡方分布.同时,得到了参数的极大经验似然估计和广义最小二乘估计的渐近分布.通过数值模拟分析,可知经验似然方法在覆盖率和置信区域大小方面均优于正态逼近方法.In order to study the confidence region of the parameters for the partially linear errors-in-variables models with longitudinal data,using the empirical likelihood method to construct empirical likelihood ratio statistics,it is proved that the limit distribution of the statistics is thechi-square distribution.Meanwhile,the asymptotic distributions of the maximum empirical likelihood estimator and the generalized least squares estimator of the parameters are obtained.By the analysis of numerical simulations,it is known that the empirical likelihood method is superior to the normal approximation methods in terms of coverage probabilities and confidence regions.

关 键 词：经验似然 测量误差 置信域 部分线性模型 纵向数据 

分 类 号：O212.1[理学—概率论与数理统计]