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

84 Pages Posted: 22 Nov 2016

See all articles by Alexander Chudik

Alexander Chudik

Federal Reserve Banks - Federal Reserve Bank of Dallas

George Kapetanios

King's College, London

M. Hashem Pesaran

University of Southern California - Department of Economics; University of Cambridge - Trinity College (Cambridge)

Date Written: 2016-11-01

Abstract

Model specification and selection are recurring themes in econometric analysis. Both topics become considerably more complicated in the case of large-dimensional data sets where the set of specification possibilities can become quite large. In the context of linear regression models, penalised regression has become the de facto benchmark technique used to trade off parsimony and fit when the number of possible covariates is large, often much larger than the number of available observations. However, issues such as the choice of a penalty function and tuning parameters associated with the use of penalized regressions remain contentious. In this paper, we provide an alternative approach that considers the statistical significance of the individual covariates one at a time, whilst 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. The OCMT provides an alternative to penalised regression methods: It is based on statistical inference and is therefore easier to interpret and relate to the classical statistical analysis, it allows working under more general assumptions, it is faster, and performs well in small samples for almost all of the different sets of experiments considered in this paper. We provide extensive theoretical and Monte Carlo results in support of adding the proposed OCMT model selection procedure to the toolbox of applied researchers. The usefulness of OCMT is also illustrated by an empirical application to forecasting U.S. output growth and inflation.

JEL Classification: C52, C55

Suggested Citation

Chudik, Alexander and Kapetanios, George and Pesaran, M. Hashem, A One-Covariate at a Time, Multiple Testing Approach to Variable Selection in High-Dimensional Linear Regression Models (2016-11-01). Globalization and Monetary Policy Institute Working Paper No. 290, Available at SSRN: https://ssrn.com/abstract=2874165 or http://dx.doi.org/10.24149/gwp290

Alexander Chudik (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of Dallas ( email )

2200 North Pearl Street
PO Box 655906
Dallas, TX 75265-5906
United States

George Kapetanios

King's College, London ( email )

30 Aldwych
London, WC2B 4BG
United Kingdom
+44 20 78484951 (Phone)

M. Hashem Pesaran

University of Southern California - Department of Economics

3620 South Vermont Ave. Kaprielian (KAP) Hall 300
Los Angeles, CA 90089
United States

University of Cambridge - Trinity College (Cambridge) ( email )

United Kingdom

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
153
Abstract Views
734
rank
235,021
PlumX Metrics