A Root-n Consistent Backktting Estimator for Semiparametric Additive Modelling

We explore additive models that combine both parametric and nonparamet-ric terms and propose a p n-consistent backktting estimator for the parametric component of the model. The theoretical properties of the estimator are developed for the case with a single nonparametric term and extended to an arbitrary number of nonparametric additive terms. An estimator for the optimal band-width making minimal use of asymptotic expressions for bias and variance is proposed, and a fast implementation algorithm for model tting and bandwidth selection is developed. The practical behavior of the estimator and bandwidth selection is illustrated by simulation experiments.