Model selection for high dimensional nonparametric additive models via ridge estimation

Abstract: In ultrahigh dimensional data analysis, to keep computational performance well and good
statistical properties still working, nonparametric additive models face increasing challenges. To
overcome them, we introduce a methodology of model selection for high dimensional nonparametric
additive models. Our approach is to propose a novel group screening procedure via nonparametric
smoothing ridge estimation (GRIE) to find the importance of each covariate. It is then combined
with the sure screening property of GRIE and the model selection property of extended Bayesian
information criteria (EBIC) to select the suitable sub-models in nonparametric additive models.
Theoretically, we establish the strong consistency ofmodel selection for the proposedmethod. Extensive
simulations and two real datasets illustrate the outstanding performance of the GRIE-EBIC method.
Keywords: model selection; nonparametric additive models; nonparametric smoothing; ridge estimation