Likelihood identifiability and parameter estimation with nonignorable missing data

doi:10.1002/cjs.11704

	Likelihood identifiability and parameter estimation with nonignorable missing data
	ZHENG, Siming 1,2; ZHANG, Juan 3; ZHOU, Yong 4,5
刊名	CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
	2022-05-27
页码	20
关键词	Equivalent asymptotic efficiency exponentially tilting generalized method of moments identifiability nonignorable missingness
ISSN号	0319-5724
DOI	10.1002/cjs.11704
英文摘要	We identify sufficient conditions to resolve the identification problem under nonignorable missingness, especially the identifiability of the observed likelihood when some of the covariate values are missing not at random, or, simultaneously, the response is also missing not at random. It is more difficult to tackle these cases than the nonignorable nonresponse case, and, to the best of our knowledge, the simultaneously missing case has never been discussed before. Under these conditions, we propose some parameter estimation methods. As an illustration, when some of the covariate values are missing not at random, we adopt a semiparametric logistic model with a tilting parameter to model the missingness mechanism and use an imputed estimating equation based on the generalized method of moments to estimate the parameters of interest and the tilting parameter simultaneously. This approach avoids the requirement for other independent surveys or a validation sample to estimate the unknown tilting parameter. The asymptotic properties of our proposed estimators are derived, and the proofs can be modified to show that our methods of estimation, which are based on inverse probability weighting, augmented inverse probability weighting, and estimating equation projection, have the same asymptotic efficiency when the tilting parameter is either known or unknown but estimated by some other method. In simulation studies, we compare our methods with various alternative approaches and find that our methods are more robust and effective.
资助项目	National Key Research and Development Program of China[2021YFA1000100] ; National Key Research and Development Program of China[2021YFA1000101] ; State Key Program of National Natural Science Foundation of China[71931004]
WOS研究方向	Mathematics
语种	英语
出版者	WILEY
WOS记录号	WOS:000800633000001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61408]
专题	中国科学院数学与系统科学研究院
通讯作者	ZHOU, Yong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 2.City Univ Hong Kong, Dept Management Sci, Hong Kong, Peoples R China 3.Capital Univ Econ & Business, Sch Stat, Beijing, Peoples R China 4.Key Lab Adv Theory & Applicat Stat & Data Sci, MOE, Shanghai, Peoples R China 5.East China Normal Univ, Acad Stat & Interdisciplinary Sci, Shanghai, Peoples R China
推荐引用方式 GB/T 7714	ZHENG, Siming,ZHANG, Juan,ZHOU, Yong. Likelihood identifiability and parameter estimation with nonignorable missing data[J]. CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE,2022:20.
APA	ZHENG, Siming,ZHANG, Juan,&ZHOU, Yong.(2022).Likelihood identifiability and parameter estimation with nonignorable missing data.CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE,20.
MLA	ZHENG, Siming,et al."Likelihood identifiability and parameter estimation with nonignorable missing data".CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE (2022):20.