Efficient Estimation of a Partial Linear Model Under Heteroskedasticity with Unknown Form

Abstract

In this paper we consider the series estimator for the partial linear regression model proposed in Li (2000) to allow for heteroskedastictiy with unknown form. We propose an alternative estimator and prove that it achieves Chamberlain's (1992) semi-parametric efficiency bound. The proposed estimator shares the same first-order asymptotic properties as Li (2000). The Monte Carlo experiment shows that our estimator behaves in a way that is quite similar to Li (2000) estimator. To overcome the problem of picking smoothing parameters in series estimation, we propose minimizing the bootstrapping approximate mean square error to choose the smoothing parameters. By using the true mean square error as the benchmark, the bootstrap method works well and provides us with the criteria to choose two smoothing parameters simultaneously.