An efficient marginal integration estimator of a semiparametric additive modelling

In this paper we introduce estimators for the nonparametric and the finite dimensional components of a partially additive model. In a first step the parametric part is estimated through an instrumental variable method. Then the nonparametric additive components are estimated by inserting the preliminary marginal integration estimator in a one step backfitting algorithm. The resulting estimators are efficient in the sense that it has the same asymptotic bias and variance as if the parametric and the other nonparametric components were known.