Abstract
We consider a single-step approach to estimating the parametric coefficients and bandwidth parameters in a partially linear model. We establish a direct connection between this estimator and the two-step estimator of Robinson (1988). Simulations show that the resulting estimator improves recovery of the nonparametric component and the fitted conditional mean in most designs, while delivering coefficient estimates that are typically comparable to Robinson’s two-step estimator.
•Develops a single-step cross-validation estimator for the partially linear model.•Shows equivalence to a common-bandwidth version of Robinson’s estimator.•Derives the coefficient-targeted common-bandwidth rate for Robinson’s estimator.•Finds improved recovery of m(.) and the fitted conditional mean in simulations.