Linear Model Selection When Covariates Contain Errors

Xinyu Zhang, Haiying Wang, Yanyuan Ma, Raymond J. Carroll

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Prediction precision is arguably the most relevant criterion of a model 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.

Original languageEnglish (US)
Pages (from-to)1553-1561
Number of pages9
JournalJournal of the American Statistical Association
Volume112
Issue number520
DOIs
StatePublished - Oct 2 2017

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Model Selection
Covariates
Linear Model
Measurement Error
Selection Procedures
Linear Regression Model
Prediction
Prediction Error
Model
Unknown Parameters
Optimality
Regression
Moment
Model selection
Evaluation
Measurement error
Linear regression model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Zhang, Xinyu ; Wang, Haiying ; Ma, Yanyuan ; Carroll, Raymond J. / Linear Model Selection When Covariates Contain Errors. In: Journal of the American Statistical Association. 2017 ; Vol. 112, No. 520. pp. 1553-1561.
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Linear Model Selection When Covariates Contain Errors. / Zhang, Xinyu; Wang, Haiying; Ma, Yanyuan; Carroll, Raymond J.

In: Journal of the American Statistical Association, Vol. 112, No. 520, 02.10.2017, p. 1553-1561.

Research output: Contribution to journalArticle

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