Automatic structure recovery for additive models.

We propose an automatic structure recovery method for additive models, based on a backfitting algorithm coupled with local polynomial smoothing, in conjunction with a new kernel-based variable selection strategy. Our method produces estimates of the set of noise predictors, the sets of predictors that contribute polynomially at different degrees up to a specified degree , and the set of predictors that contribute beyond polynomially of degree . We prove consistency of the proposed method, and describe an extension to partially linear models. Finite-sample performance of the method is illustrated via Monte Carlo studies and a real-data example.