非线性半参数回归模型中参数的经验似然置信域

数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1338-1349.

非线性半参数回归模型中参数的经验似然置信域

洛阳师范学院数学科学学院河南洛阳 |471022；北京工业大学应用数理学院北京 100022

收稿日期:2007-10-09 修回日期:2008-12-30 出版日期:2009-10-25 发布日期:2009-10-25
基金资助:
国家自然科学基金(10571008)、中国博士后科学基金(20080430633)和河南省自然科学研究项目(2008B110009)资助

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

College of Mathematics and Science, Luoyang Normal University, |Henan Luoyang 471022；College of Applied Sciences, Beijing University of Technology, Beijing 100022

Received:2007-10-09 Revised:2008-12-30 Online:2009-10-25 Published:2009-10-25
Supported by:
国家自然科学基金(10571008)、中国博士后科学基金(20080430633)和河南省自然科学研究项目(2008B110009)资助

摘要/Abstract

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Χ²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.

关键词: 非线性半参数回归模型, 经验似然, Χ²分布, 置信域

Abstract:

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.

Key words: Nonlinear semiparametric regression model, Empirical likelihood, Chi-square distribution, Confidence region

中图分类号:

62G05

冯三营, 薛留根, 范承华. 非线性半参数回归模型中参数的经验似然置信域[J]. 数学物理学报, 2009, 29(5): 1338-1349.

FENG San-Ying, XUE Liu-Gen, FAN Cheng-Hua. Empirical Likelihood Confidence Regions of the Parameters in Nonlinear Semiparametric Regression Models[J]. Acta mathematica scientia,Series A, 2009, 29(5): 1338-1349.

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