  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.
