A one-covariate-at-a-time multiple testing approach to variable selection in additive models

Liangjun Su (), Thomas Tao Yang, Yonghui Zhang and Qiankun Zhou

Econometric Reviews, 2024, vol. 43, issue 9, 671-712

Abstract: This article proposes a One-Covariate-at-a-time Multiple Testing (OCMT) approach to choose significant variables in high-dimensional nonparametric additive regression models. Similarly to Chudik, Kapetanios, and Pesaran, we consider the statistical significance of individual nonparametric additive components one at a time and take into account the multiple testing nature of the problem. Both one-stage and multiple-stage procedures are considered. The former works well in terms of the true positive rate only if the net effects of all signals are strong enough; the latter helps to pick up hidden signals that have weak net effects. Simulations demonstrate the good finite-sample performance of the proposed procedures. As an empirical illustration, we apply the OCMT procedure to a dataset extracted from the Longitudinal Survey on Rural Urban Migration in China. We find that our procedure works well in terms of out-of-sample root mean square forecast errors, compared with competing methods such as adaptive group Lasso (AGLASSO).

Date: 2024
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DOI: 10.1080/07474938.2024.2357771

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