Linear Model Selection When Covariates Contain Errors

doi:10.1080/01621459.2016.1219262

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	Linear Model Selection When Covariates Contain Errors
	Zhang, Xinyu1 ; Wang, Haiying 2; Ma, Yanyuan 3; Carroll, Raymond J.4,5
	2017
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
卷号	112 期号:520 页码:1553-1561
摘要	Prediction 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.
关键词	Errors in covariates Loss efficiency Measurement error Model selection Selection consistency
DOI	10.1080/01621459.2016.1219262
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000423299400019
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29435
专题	系统科学研究所
通讯作者	Wang, Haiying
作者单位	1.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
推荐引用方式 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.