核实数据下反映缺失非线性EV模型的经验似然推断  

Empirical Likelihood Inference in Nonlinear EV Models Under Validation Data with Missing Response Data

作　　者：方连娣 FANG Lian-di(School of Electrical and Information Engineering,Jiangsu University,Zhengjiang 212013,China;College of Mathematics and Computer Science,Tongling University,Tongling 244000,China)

机构地区：[1]江苏大学电气信息工程学院 [2]铜陵学院数学与计算机学院

出　　处：《数学的实践与认识》2019年第18期199-208,共10页Mathematics in Practice and Theory

基　　金：安徽省高校自然科学研究项目(KJ2018A0477);安徽省高校优秀青年人才支持计划项目(gxyq2018089)

摘　　要：考虑一类带有不完全数据的非线性模型,其协变量带有测量误差且反映变量随机缺失.通过核实数据和借补数据构造了回归参数θ的估计的经验对数似然比统计量,证明了所构造的似然比函数渐近独立标准X12变量的加权和分布.在权未知的情况下,分别采用定义权的相合估计法和构造调整被估计的经验对数似然法构造出θ的渐近置信域.进一步,基于借补方法构造了反映变量均值的调整经验对数似然比统计量,并证明了统计量渐近标准X12分布,所得结果可以用来构造反映均值的置信域.A class of nonlinear model is considered with incomplete data,the covariances with measurement error and response variables.The estimated empirical log-likelihood ratio statistic for the unknown regression parameter theta is constructed with help of validation and imputation data.The estimated log-likelihood is proved to be asymptotically distributed as a weighted sums of independent chi-square variable with 1 degree of freedom.In the case of unknown weights,the asymptotic confidence region of theta is constructed by using the coincidence estimation of weights and the adjusted empirical log-likelihood.Furthermore an adjusted empirical log-likelihood approach to inference on the mean of the response variable is developed.It is proved that the proposed statistics have the asymptotic standard chi-square distribution,and hence can be used to constructing the confidence interval for the mean.

关 键 词：经验似然 反映缺失 非线性模型 相合估计 借补方法 

分 类 号：O212.1[理学—概率论与数理统计]