A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High-Dimensional Linear Regression Models

• 成果类型: Article
• 署名作者: Chudik, A.; Kapetanios, G.; Pesaran, M. Hashem
• 署名单位: Federal Reserve System - USA; Federal Reserve Bank - Dallas; University of London; King's College London; University of Southern California; University of Cambridge
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA14176
• 发表日期: 2018
• 页码: 1479-1512
• 关键词: false discovery rate; PENALIZED LIKELIHOOD; DANTZIG SELECTOR; FDR CONTROL; INDEPENDENCE; shrinkage; regularization; estimators; inference; Lasso

摘要

This paper provides an alternative approach to penalized regression for model selection in the context of high-dimensional linear regressions where the number of covariates is large, often much larger than the number of available observations. We consider the statistical significance of individual covariates one at a time, while taking full account of the multiple testing nature of the inferential problem involved. We refer to the proposed method as One Covariate at a Time Multiple Testing (OCMT) procedure, and use ideas from the multiple testing literature to control the probability of selecting the approximating model, the false positive rate, and the false discovery rate. OCMT is easy to interpret, relates to classical statistical analysis, is valid under general assumptions, is faster to compute, and performs well in small samples. The usefulness of OCMT is also illustrated by an empirical application to forecasting U.S. output growth and inflation.