协变量缺失下线性模型中参数的经验似然推断

J4 ›› 2011, Vol. 46 ›› Issue (1): 92-96.

协变量缺失下线性模型中参数的经验似然推断

王秀丽^1,2,盖玉洁²,林路²

1.山东师范大学数学院, 山东济南 250014; 2.山东大学数学院, 山东济南 250100

收稿日期:2010-04-29 出版日期:2011-12-14 发布日期:2011-03-16
作者简介:王秀丽（1976-），女，博士生，讲师，研究方向为半参数统计. Email: xiuliwang168@sina.com
基金资助:
山东省自然科学基金资助项目(Q2008A04)

Empirical likelihood inference for the parameter in linear model with missing covariates

WANG Xiu-li^{1, 2}, GAI Yu-jie², LIN Lu²

1. School of Mathematical Science, Shandong Normal University, Jinan 250014, Shandong, China;
2. School of Mathematical Science, Shandong University, Jinan 250100, Shandong, China

Received:2010-04-29 Online:2011-12-14 Published:2011-03-16

摘要/Abstract

摘要：

考虑协变量缺失下线性模型中兴趣参数的经验似然推断,利用逆概率加权的方法构造未知参数的估计函数。在一定条件下,证明了基于本文构造的估计函数的经验对数似然比趋于一个标准的卡方分布,利用这个结果可以构造参数的置信域。最后,通过数值模拟,进一步验证了结论的正确性。

关键词: 线性模型；估计函数；经验似然；置信域

Abstract:

The empirical likelihood inference for the parameter of interest in linear model with missing covariates is considered. Using the inverse probability-weighted method, the estimating function for the unknown parameter is constructed. The empirical log-likelihood ratio based on our estimating function is proved, under some suitable conditions, to be a standard chisquare distribution asymptotically. With this result, the confidence region for the parameter can be constructed. At last, our result is further verified through some numerical simulations.

Key words: linear model; estimating function; empirical likelihood; confidence region

王秀丽1,2,盖玉洁2,林路2. 协变量缺失下线性模型中参数的经验似然推断[J]. J4, 2011, 46(1): 92-96.

WANG Xiu-li1, 2, GAI Yu-jie2, LIN Lu2. Empirical likelihood inference for the parameter in linear model with missing covariates[J]. J4, 2011, 46(1): 92-96.

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