| 司世景,李二倩,田茂再.带有二元连接函数的半参数模型[J].数学年刊A辑,2015,36(2):191~208 |
| 带有二元连接函数的半参数模型 |
| Semi-parametric Model with Bivariate Link Function |
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| DOI： |
| 中文关键词: 二元连接函数, 轮廓似然, 半参数模型, 局部功效检验, 指数型分布族 |
| 英文关键词:Bivariate link function, Profile likelihood, Semi-parametric model,
Local power test, Exponential distribution family |
| 基金项目:本文受到国家自然科学基金 (No.11271368),
国家社会科学基金重点项目 (No.13AZD064), 教育部高等学校博士学科点专项科研基金(No.20130004110007), 北京市社会科学基金重大项目(No.15ZDA17)
和兰州商学院``飞天学者特聘计划''的资助. |
| Author Name | Affiliation | E-mail | | SI Shijing | Center for Applied Statistics, School of Statistics, Renmin University of China,
Beijing 100872, China. | sisingjing2006@163.com | | LI Erqian | Corresponding author. School of Statistics, Lanzhou University of Finance
and Economics, Lanzhou 730101, China
| li2qian@ruc.edu.cn | | TIAN Maozai | Center for Applied Statistics, School
of Statistics, Renmin University of China, Beijing 100872, China. | mztian@ruc.edu.cn |
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| 中文摘要: |
| 提出了一种新的带有二元连接函数的广义半参数模型, 即二元连接模型 (简称为BLM). 使用轮廓似然方法估计模型的
参数和非参数部分, 并给出了计算算法. 证明了所得的未知参数的估计量为$\sqrt{n}$-\!\!相合, 渐近正态且具有渐近最小方差,
给出了实际数据分析和模拟研究, 最终采用局部功效方法来检验非参数部分的线性性. |
| 英文摘要: |
| In this article, a new kind of the generalized semi-parametric model with the
bivariate link function, which is called the bivariate link model (BLMfor short), is developed.
The profile likelihood method is utilized to estimate the parametric part and nonparametric
part of the model and the computational algorithm is given. The resulting estimators
of the unknown coefficients are shown to be √n consistent and asymptotically Gaussianwith asymptotically minimum variances. Real data analysis and simulation study are also
presented, and finally the local power technique is employed to test the linearity of the
nonparametric part. |
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