Estimation of a partially linear additive model with generated covariates

Abstract

We propose kernel-based estimators for both the parametric and nonparametric components of a partially linear additive regression model where a subset of the covariates entering the nonparametric component are generated by the estimation of an auxiliary nonparametric regression. Both estimators are shown to be asymptotically normally distributed. The estimator for the finite dimensional parameter is shown to converge at the parametric n rate and the estimator for the infinite dimensional parameter converges at a slower nonparametric rate that, as usual, depends on the rate of decay of the bandwidths and the dimensionality of the underlying regression. A small Monte Carlo study is conducted to shed light on the finite sample performance of our estimators and to contrast them with those of estimators available in the extant literature.