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 of model selection for the proposed method. Extensive simulations and two real datasets illustrate the outstanding performance of the GRIE-EBIC method.