  Generalized additive model is a powerful statistical learning and predictive
modeling tool that has been applied in a wide range of applications. The need
of high-dimensional additive modeling is eminent in the context of dealing with
high through-put data such as genetic data analysis. In this article, we
studied a two step selection and estimation method for ultra high dimensional
generalized additive models. The first step applies group lasso on the expanded
bases of the functions. With high probability this selects all nonzero
functions without having too much over selection. The second step uses adaptive
group lasso with any initial estimators, including the group lasso estimator,
that satisfies some regular conditions. The adaptive group lasso estimator is
shown to be selection consistent with improved convergence rates. Tuning
parameter selection is also discussed and shown to select the true model
consistently under GIC procedure. The theoretical properties are supported by
extensive numerical study.
