{"title":"数据随机缺失时基于正态分布的伪极大似然估计的一致性。","authors":"Ke-Hai Yuan, Peter M Bentler","doi":"10.1198/tast.2010.09203","DOIUrl":null,"url":null,"abstract":"<p><p>This paper shows that, when variables with missing values are linearly related to observed variables, the normal-distribution-based pseudo MLEs are still consistent. The population distribution may be unknown while the missing data process can follow an arbitrary missing at random mechanism. Enough details are provided for the bivariate case so that readers having taken a course in statistics/probability can fully understand the development. Sufficient conditions for the consistency of the MLEs in higher dimensions are also stated, while the details are omitted.</p>","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2010-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1198/tast.2010.09203","citationCount":"15","resultStr":"{\"title\":\"Consistency of Normal Distribution Based Pseudo Maximum Likelihood Estimates When Data Are Missing at Random.\",\"authors\":\"Ke-Hai Yuan, Peter M Bentler\",\"doi\":\"10.1198/tast.2010.09203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>This paper shows that, when variables with missing values are linearly related to observed variables, the normal-distribution-based pseudo MLEs are still consistent. The population distribution may be unknown while the missing data process can follow an arbitrary missing at random mechanism. Enough details are provided for the bivariate case so that readers having taken a course in statistics/probability can fully understand the development. Sufficient conditions for the consistency of the MLEs in higher dimensions are also stated, while the details are omitted.</p>\",\"PeriodicalId\":50801,\"journal\":{\"name\":\"American Statistician\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2010-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1198/tast.2010.09203\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Statistician\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1198/tast.2010.09203\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Statistician","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1198/tast.2010.09203","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Consistency of Normal Distribution Based Pseudo Maximum Likelihood Estimates When Data Are Missing at Random.
This paper shows that, when variables with missing values are linearly related to observed variables, the normal-distribution-based pseudo MLEs are still consistent. The population distribution may be unknown while the missing data process can follow an arbitrary missing at random mechanism. Enough details are provided for the bivariate case so that readers having taken a course in statistics/probability can fully understand the development. Sufficient conditions for the consistency of the MLEs in higher dimensions are also stated, while the details are omitted.
期刊介绍：
Are you looking for general-interest articles about current national and international statistical problems and programs; interesting and fun articles of a general nature about statistics and its applications; or the teaching of statistics? Then you are looking for The American Statistician (TAS), published quarterly by the American Statistical Association. TAS contains timely articles organized into the following sections: Statistical Practice, General, Teacher''s Corner, History Corner, Interdisciplinary, Statistical Computing and Graphics, Reviews of Books and Teaching Materials, and Letters to the Editor.
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