We propose an automatic structure recovery scheme for additive models. The structure recovery
is based on a backfitting algorithm coupled with local polynomial smoothing, in conjunction
with a new kernel-based variable selection strategy. The automatic structure recovery method
produces estimates of the set of noise predictors, the sets of predictors that contribute
polynomially at different orders up to any given order, and the set of predictors that contribute
beyond polynomially. Asymptotic consistency of the method is proved. An extension to partially
linear models is also described. Finite-sample performance of the proposed methods is illustrated
via Monte Carlo studies and real data examples.