缺失数据下非线性EV模型参数的经验似然置信域

数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 233-245.

缺失数据下非线性EV模型参数的经验似然置信域

刘强, 薛留根

首都经济贸易大学统计学院北京 100070|北京工业大学应用数理学院北京 100022

收稿日期:2009-05-20 修回日期:2011-03-07 出版日期:2012-02-25 发布日期:2012-02-25
基金资助:
国家社科基金项目(10CTJ001)、北京市教委社科计划项目(SM201110038014)和北京市属高等学校人才强教计划-中青年骨干人才培养计划(PHR201008214)资助

Empirical Likelihood Confidence Regions of Parameters in Nonlinear EV Models under Missing Data

LIU Qiang, XUE Liu-Gen

School of Statistics, Capital University of Economics and Business, Beijing 100070|College of Applied Sciences, Beijing University of Technology, Beijing 100022

Received:2009-05-20 Revised:2011-03-07 Online:2012-02-25 Published:2012-02-25
Supported by:
国家社科基金项目(10CTJ001)、北京市教委社科计划项目(SM201110038014)和北京市属高等学校人才强教计划-中青年骨干人才培养计划(PHR201008214)资助

摘要/Abstract

摘要：

考虑解释变量带有测量误差且响应变量随机缺失情形下的非线性EV模型. 通过利用核实数据, 构造了未知参数的两种经验对数似然比统计量. 证明了所构造统计量的分布渐近于χ²分布, 所得结果可以用来构造未知参数的渐近置信域.

关键词: 非线性EV模型, , 经验似然, 核实数据, 缺失数据

Abstract:

The missing response problem in the nonlinear EV(error-in-variables) models is considered, where the explanatory variate X is erroneously measured. With the help of val-idation data, two empirical log-likelihood ratio statistics for the unknown parameters in the model are proposed. It is proved that the proposed statistics are asymptotically chi-square distribution under some mild conditions, and hence can be used to constructing the confidence regions of the parameters.

Key words: Nonlinear EV models, Empirical likelihood, Validation data, Missing data

中图分类号:

62G05

刘强, 薛留根. 缺失数据下非线性EV模型参数的经验似然置信域[J]. 数学物理学报, 2012, 32(1): 233-245.

LIU Qiang, XUE Liu-Gen. Empirical Likelihood Confidence Regions of Parameters in Nonlinear EV Models under Missing Data[J]. Acta mathematica scientia,Series A, 2012, 32(1): 233-245.

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