| 部分函数线性模型的经验似然推断 |
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| 引用本文： | 胡玉萍,冯三营,薛留根.部分函数线性模型的经验似然推断[J].应用概率统计,2015,31(2):146-158. |
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| 作者姓名： | 胡玉萍 冯三营 薛留根 |
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| 作者单位： | 北京工业大学应用数理学院, 郑州大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金(11171012,11331011);高等学校博士学科点专项科研基金(20121103110004);全国统计科学研究重点项目(2014LZ45);河南省科技厅基础与前沿研究(122300413202);北京工业大学第十三届研究生科技基金重点项目(ykj-2014-10722);北京工业大学博士生创新基金资助 |
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| 摘 要： | 本文考虑部分函数线性回归模型,研究了回归系数的经验似然推断,证明了所提出的经验对数似然比渐近于χ~2分布,此结果可以用来构造了相应兴趣参数的置信域.另外,本文也给出了系数函数的极大经验似然估计,并在适当条件下给出了所提出估计量的收敛速度.仅就置信域精度及其覆盖概率大小方面,通过模拟研究和实例分析比较了经验似然方法与最小二乘方法的优劣.
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| 关 键 词： | 部分函数线性模型 经验似然 函数型数据 置信域. |
Empirical Likelihood Inference for Partial Functional Linear Model |
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| Hu Yuping,Feng Sanying,Xue Liugen.Empirical Likelihood Inference for Partial Functional Linear Model[J].Chinese Journal of Applied Probability and Statisties,2015,31(2):146-158. |
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| Authors: | Hu Yuping Feng Sanying Xue Liugen |
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| Institution: | School of Applied Sciences, Beijing University of Technology; School of Mathematics and Statistics, Zhengzhou University |
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| Abstract: | In this paper, we consider the partial functional linear regression
model, and construct the empirical log-likelihood ratio statistic for the unknown regression
parameter. It is shown that the proposed statistics have the asymptotic standard chi-square
distribution, and hence they can be used to construct the confidence region of the parameter.
In addition, the maximum empirical likelihood estimator of the unknown coefficient function
is constructed, and its asymptotic behavior is proved. A simulation study and real data
analysis are 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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