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A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High‐Dimensional Linear Regression Models
Author(s) -
Chudik A.,
Kapetanios G.,
Pesaran M. Hashem
Publication year - 2018
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta14176
Subject(s) - covariate , linear regression , statistics , econometrics , proper linear model , linear model , selection (genetic algorithm) , mathematics , feature selection , regression analysis , variable (mathematics) , computer science , bayesian multivariate linear regression , artificial intelligence , mathematical analysis
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.