We study the heteroscedastic partially linear model with an unspecified partial baseline component and a nonparametric variance function. An interesting finding is that the performance of a naive weighted version of the existing estimator could deteriorate when the smooth baseline component is badly estimated. To avoid this, we propose a family of consistent estimators and investigate their asymptotic properties. We show that the optimal semiparametric efficiency bound can be reached by a semiparametric kernel estimator in this family. Building upon our theoretical findings and heuristic arguments about the equivalence between kernel and spline smoothing, we conjecture that a weighted partial-spline estimator could also be semiparametric efficient. Properties of the proposed estimators are presented through theoretical illustration and numerical simulations.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)
- Statistics, Probability and Uncertainty
- Applied Mathematics