  Thanks to its fine balance between model flexibility and interpretability,
the nonparametric additive model has been widely used, and variable selection
for this type of model has been frequently studied. However, none of the
existing solutions can control the false discovery rate (FDR) unless the sample
size tends to infinity. The knockoff framework is a recent proposal that can
address this issue, but few knockoff solutions are directly applicable to
nonparametric models. In this article, we propose a novel kernel knockoffs
selection procedure for the nonparametric additive model. We integrate three
key components: the knockoffs, the subsampling for stability, and the random
feature mapping for nonparametric function approximation. We show that the
proposed method is guaranteed to control the FDR for any sample size, and
achieves a power that approaches one as the sample size tends to infinity. We
demonstrate the efficacy of our method through intensive simulations and
comparisons with the alternative solutions. Our proposal thus makes useful
contributions to the methodology of nonparametric variable selection, FDR-based
inference, as well as knockoffs.
