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Linear Model Selection When Covariates Contain Errors
Zhang, Xinyu1; Wang, Haiying2; Ma, Yanyuan3; Carroll, Raymond J.4,5
AbstractPrediction precision is arguably the most relevant criterion of amodel in practice and is often a sought after property. A common difficulty with covariates measured with errors is the impossibility of performing prediction evaluation on the data even if a model is completely given without any unknown parameters. We bypass this inherent difficulty by using special properties on moment relations in linear regression models with measurement errors. The end product is a model selection procedure that achieves the same optimality properties that are achieved in classical linear regression models without covariate measurement error. Asymptotically, the procedure selects the model with the minimum prediction error in general, and selects the smallest correct model if the regression relation is indeed linear. Our model selection procedure is useful in prediction when future covariates without measurement error become available, for example, due to improved technology or better management and design of data collection procedures. Supplementary materials for this article are available online.
KeywordErrors in covariates Loss efficiency Measurement error Model selection Selection consistency
Funding ProjectNational Natural Science Foundation of China[71522004] ; National Natural Science Foundation of China[11471324] ; National Natural Science Foundation of China[71631008] ; National Science Foundation[DMS-1608540] ; National Cancer Institute[U01-CA057030]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000423299400019
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Document Type期刊论文
Corresponding AuthorWang, Haiying
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
2.Univ New Hampshire, Dept Math & Stat, Durham, NH 03824 USA
3.Penn State Univ, Dept Stat, State Coll, PA USA
4.Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA
5.Univ Technol Sydney, Sch Math & Phys Sci, Broadway, NSW, Australia
Recommended Citation
GB/T 7714
Zhang, Xinyu,Wang, Haiying,Ma, Yanyuan,et al. Linear Model Selection When Covariates Contain Errors[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2017,112(520):1553-1561.
APA Zhang, Xinyu,Wang, Haiying,Ma, Yanyuan,&Carroll, Raymond J..(2017).Linear Model Selection When Covariates Contain Errors.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,112(520),1553-1561.
MLA Zhang, Xinyu,et al."Linear Model Selection When Covariates Contain Errors".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 112.520(2017):1553-1561.
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