Kernel estimation of a partially linear additive model

In this paper, we introduce a kernel estimator for the finite-dimensional parameter of a partially linear additive model. Under some regularity conditions, we establish n1/2-consistency and asymptotic normality of the estimator. Unlike existing kernel-based estimators: Fan et al. (1998. Ann. Statist. 26, 943-971) and Fan and Li (2003. Statist. Sinica 13, 739-762) our estimator attains the semiparametric efficiency bound of the partially linear additive model under homoscedastic errors. We also show that when the true specification is the partially linear additive model, the proposed estimator is asymptotically more efficient than an estimator that ignores the additive structure.