Linear Model Selection When Covariates Contain Errors

• 成果类型: Article
• 署名作者: Zhang, Xinyu; Wang, Haiying; Ma, Yanyuan; Carroll, Raymond J.
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University System Of New Hampshire; University of New Hampshire; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Texas A&M University System; Texas A&M University College Station; University of Technology Sydney
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1219262
• 发表日期: 2017
• 页码: 1553-1561
• 关键词: VARIABLE SELECTION; Cross-validation; prediction

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.