Empirical likelihood confidence bands for distribution functions with missing responses

doi:10.1016/j.jspi.2010.03.044

CSpace > 应用数学研究所

	Empirical likelihood confidence bands for distribution functions with missing responses
	Wang, Qihua1 ; Qin, Yongsong 2
	2010-09-01
发表期刊	JOURNAL OF STATISTICAL PLANNING AND INFERENCE
ISSN	0378-3758
卷号	140 期号:9 页码:2778-2789
摘要	Distribution function estimation plays a significant role of foundation in statistics since the population distribution is always involved in statistical inference and is usually unknown. In this paper, we consider the estimation of the distribution function of a response variable Y with missing responses in the regression problems. It is proved that the augmented inverse probability weighted estimator converges weakly to a zero mean Gaussian process. A augmented inverse probability weighted empirical log-likelihood function is also defined. It is shown that the empirical log-likelihood converges weakly to the square of a Gaussian process with mean zero and variance one. We apply these results to the construction of Gaussian process approximation based confidence bands and empirical likelihood based confidence bands of the distribution function of Y. A simulation is conducted to evaluate the confidence bands. (C) 2010 Elsevier B.V. All rights reserved.
关键词	Imputation Inverse probability weighting Confidence bands Empirical likelihood Missing at random
DOI	10.1016/j.jspi.2010.03.044
语种	英语
资助项目	National Science Fund for Distinguished Young Scholars in China[10725106] ; National Natural Science Foundation of China[10671198] ; National Natural Science Foundation of China[10971038] ; National Science Fund for Creative Research Groups in China ; Key Lab of Complex Structure and Data Science ; Research Grants Council of the Hong Kong[HKU 7050/06P]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000278398300039
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9814
专题	应用数学研究所
通讯作者	Wang, Qihua
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Guangxi Normal Univ Guilin, Sch Math Sci, Guangxi 541004, Peoples R China
推荐引用方式 GB/T 7714	Wang, Qihua,Qin, Yongsong. Empirical likelihood confidence bands for distribution functions with missing responses[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE,2010,140(9):2778-2789.
APA	Wang, Qihua,&Qin, Yongsong.(2010).Empirical likelihood confidence bands for distribution functions with missing responses.JOURNAL OF STATISTICAL PLANNING AND INFERENCE,140(9),2778-2789.
MLA	Wang, Qihua,et al."Empirical likelihood confidence bands for distribution functions with missing responses".JOURNAL OF STATISTICAL PLANNING AND INFERENCE 140.9(2010):2778-2789.