缺失数据下半参数变系数部分线性模型的统计推断

数学物理学报 ›› 2015, Vol. 35 ›› Issue (2): 345-358.

缺失数据下半参数变系数部分线性模型的统计推断

陈盼盼^1,2, 冯三营¹, 薛留根¹

1. 北京工业大学应用数理学院北京 100124;
2. 广西科技信息网络中心南宁 530022

收稿日期:2012-05-17 修回日期:2014-06-27 出版日期:2015-04-25 发布日期:2015-04-25
通讯作者: 薛留根 E-mail:lgxue@bjut.edu.cn
作者简介:陈盼盼,E-mail:smile2668@163.com
基金资助:
国家自然科学基金(11331011)、高等学校博士学科点专项科研基金(20121103110004)、北京市自然科学基金(1142003)、北京市自然科学基金与北京市科学技术研究院联合资助项目(L140003)和北京工业大学博士创新基金资助

Statistical Inference for Semiparametric Varying Coefficient Partially Linear Model with Missing Data

Chen Panpan^1,2, Feng Sanying¹, Xue Liugen¹

1. College of Applied Sciences, Beijing University of Technology, Beijing 100124;
2. Guangxi Science &|Technology Information Network Center, Nanning 530022

Received:2012-05-17 Revised:2014-06-27 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

该文研究协变量随机缺失下半参数变系数部分线性模型的统计推断. 利用逆概率加权最小二乘方法给出了模型中参数分量和非参数分量的估计, 并证明了它们的渐近正态性. 另外该文又提出了一个逆概率加权经验对数似然比统计量, 并证明该统计量服从标准χ²分布, 从而构造了模型中参数分量的经验似然置信域. 最后通过模拟研究和实例分析说明该文提出的方法具有较好的有限样本性质.

关键词: 半参数变系数部分线性模型, 缺失数据, 逆概率加权, 渐近正态性, 经验似然

Abstract:

In this paper, we consider the statistical inference for semiparametric varying coefficient partially linear model with covariates missing at random. The profile least-squares estimators for the unknown parametric and coefficient functions are obtained by inverse probability weighted least-squares method. The asymptotic normality of the proposed estimators are proved under some appropriate conditions. In addition, we constructed an empirical log-likelihood ratio statistic for the unknown parametric components, and it is shown that the proposed statistic has the asymptotic chi-square distribution, and hence it can be used to construct the confidence regions of the parameter. Simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed procedure.

Key words: Semiparametric varying coefficient partially linear model, Missing data, Inverse probability weighted, Asymptotic normality, Empirical likelihood

中图分类号:

O212.7

陈盼盼, 冯三营, 薛留根. 缺失数据下半参数变系数部分线性模型的统计推断[J]. 数学物理学报, 2015, 35(2): 345-358.

Chen Panpan, Feng Sanying, Xue Liugen. Statistical Inference for Semiparametric Varying Coefficient Partially Linear Model with Missing Data[J]. Acta mathematica scientia,Series A, 2015, 35(2): 345-358.

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