核实数据下非线性半参数EV模型的经验似然推断  

Empirical Likelihood Inference in Nonlinear Semiparametric EV Models with Validation Data

作　　者：薛留根[1] 

机构地区：[1]北京工业大学应用数理学院,北京100022

出　　处：《数学学报（中文版）》2006年第1期145-154,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10571008)北京市自然科学基金资助项目(1042002)北京市教委科技发展计划(KM200510005009)北京市优秀人才专项经费(20041D0501515)资助项目

摘　　要：考虑带有协变量误差的非线性半参数模型,借助于核实数据,本文构造了未知参数的三种经验对数似然比统计量,证明了所提出的统计量具有渐近X2分布,此结果可以用来构造未知参数的置信域．另外,本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．仅就置信域及其覆盖概率的大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣．Consider the nonlinear semiparametric model with errors in covariables, we construct three empirical log-likelihood ratio statistics for the unknown parameter with the help of validation data. It is shown that the proposed statistics have the asymptotic chi-square distribution, and hence the confidence regions of the parameter can be constructed accordingly. In addition, the least squares estimator of unknown parameter is constructed, and its asymptotic behaviors are 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EV模型 经验似然 核实数据 

分 类 号：O212.7[理学—概率论与数理统计]