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

TY - JOUR

T1 - A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High-Dimensional Linear Regression Models

AU - Chudik, Alexander

AU - Kapetanios, George

AU - Pesaran, M. Hashem

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

U2 - 10.3982/ECTA14176

DO - 10.3982/ECTA14176

M3 - Article

SN - 0012-9682

VL - 86

SP - 1479

EP - 1512

JO - Econometrica

JF - Econometrica

IS - 4

ER -