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| 非线性半参数EV模型的经验似然置信域 | |
| 引用本文： | 冯三营,李高荣,薛留根,陈放.非线性半参数EV模型的经验似然置信域[J].高校应用数学学报(A辑),2010,25(1). |
| 作者姓名： | 冯三营 李高荣 薛留根 陈放 |
| 作者单位： | 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,北京,100124 3. 广州南洋理工学院基础部,广东广州,510980 |
| 基金项目： | 国家自然科学基金，北京市自然科学基金，高等学校博士学科点专项科研基金，北京市属市管高等学校人才强教计划，北京工业大学自然科学基础研究基金，北京工业大学博士启动基金和河南省教育厅自然科学研究 |
| 摘 要： | 考虑非参数协变量带有测量误差的非线性半参数模型,构造了模型中未知参数的经验对数似然比统计量,在测量误差分布为普通光滑分布时,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.就置信域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： | 测量误差 非线性半参数模型 经验似然 普通光滑 置信域 |
Empirical likelihood confidence regions m a nonlinear semiparametric EV models |
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| FENG San-ying,LI Gao-rong,XUE Liu-gen,CHEN Fang.Empirical likelihood confidence regions m a nonlinear semiparametric EV models[J].Applied Mathematics A Journal of Chinese Universities,2010,25(1). | |
| Authors: | FENG San-ying LI Gao-rong XUE Liu-gen CHEN Fang |
| Abstract: | In this paper, authors consider the nonlinear semiparametric models with measure-ment error in the nonparametric part, and construct the empirical log-likelihood ratio statistic for the unknown parameter. When the error is ordinary smooth, it is shown that the proposed statistics have the asymptotic standard chi-squared distribution, and hence they 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 method with the least-squares method in terms of the confidence regions and their coverage probabilities. |
| Keywords: | errors in variables nonlinear semiparametric model empirical likelihood ordinary smooth confidence region |
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