| 非线性半参数回归模型中参数的经验似然置信域 |
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| 引用本文： | 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(A辑),2009,29(5):1338-1349. |
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| 作者姓名： | 冯三营 薛留根 范承华 |
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| 作者单位： | 冯三营(洛阳师范学院数学科学学院,河南洛阳,471022);薛留根,范承华(北京工业大学应用数理学院,北京,100022) |
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| 基金项目： | 国家自然科学基金，中国博士后科学基金，河南省自然科学研究项目 |
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| 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.
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| 关 键 词： | 非线性半参数回归模型 经验似然 Χ2分布 置信域 |
| 收稿时间： | 2007-10-09 |
| 修稿时间： | 2008-12-30 |
Empirical Likelihood Confidence Regions of the Parameters in Nonlinear Semiparametric Regression Models |
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| Institution: | College of Mathematics and Science, Luoyang Normal University, |Henan Luoyang 471022；College of Applied Sciences, Beijing University of Technology, Beijing 100022 |
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| 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. |
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| Keywords: | Nonlinear semiparametric regression modelzz Empirical likelihoodzz Chi-square distributionzz Confidence regionzz |
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