非线性半参数回归模型中参数的经验似然置信域  

Empirical Likelihood Confidence Regions of the Parameters in Nonlinear Semiparametric Regression Models

作　　者：冯三营[1] 薛留根[2] 范承华[2] 

机构地区：[1]洛阳师范学院数学科学学院,河南洛阳471022 [2]北京工业大学应用数理学院,北京100022

出　　处：《数学物理学报（A辑）》2009年第5期1338-1349,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(10571008);中国博士后科学基金(20080430633);河南省自然科学研究项目(2008B110009)资助

摘　　要：该文考虑非线性半参数回归模型,构造了模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近x^2分布,由此结果可以用来构造未知参数的置信域.另外,该文也构造了未知参数的最小二乘估计量,并证明了它的渐近性质.仅就置信域精度及其覆盖概率大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣.In this paper,we consider the nonlinear semiparametric regression model,and construct the empirical log-likelihood ratio statistic for the unknown parameter.It is shown that the proposed statistics have the asymptotic standard chi-square distribution,and hence it can be used to construct the confidence region of the parameter.In addition,the least squares estimator of unknown parameter is constructed,and its asymptotic behavior is proved. A simulation study is carried out to compare the proposed methods with the least-squares method in terms of the confidence regions and its coverage probabilities.

关 键 词：非线性半参数回归模型 经验似然 X^2分布 置信域 

分 类 号：O212.7[理学—概率论与数理统计]