A One-Covariate-at-a-Time Method for Nonparametric Additive Models

Abstract: This paper 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 (2018), 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. One-stage and multiple-stage procedures are both considered. The former works well in terms of the true positive rate only if the marginal effects of all signals are strong enough; the latter helps to pick up hidden signals that have weak marginal effects. Simulations demonstrate the good finite sample performance of the proposed procedures. As an empirical application, we use the OCMT procedure on a dataset we extracted from the Longitudinal Survey on Rural Urban Migration in China. We find that our procedure works well in terms of the out-of-sample forecast root mean square errors, compared with competing methods.