{"title":"Likelihood identifiability and parameter estimation with nonignorable missing data","authors":"Siming Zheng, Juan Zhang, Yong Zhou","doi":"10.1002/cjs.11704","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":55281,"journal":{"name":"Canadian Journal of Statistics-Revue Canadienne De Statistique","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Statistics-Revue Canadienne De Statistique","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cjs.11704","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
The Canadian Journal of Statistics is the official journal of the Statistical Society of Canada. It has a reputation internationally as an excellent journal. The editorial board is comprised of statistical scientists with applied, computational, methodological, theoretical and probabilistic interests. Their role is to ensure that the journal continues to provide an international forum for the discipline of Statistics.
The journal seeks papers making broad points of interest to many readers, whereas papers making important points of more specific interest are better placed in more specialized journals. The levels of innovation and impact are key in the evaluation of submitted manuscripts.