Monday, March 3, 2003 Optimal estimators for semiparametric regression models
Ursula U. Mueller, University of Bremen
Smooth functionals of densities or regression functions can be
estimated by plugging an appropriate function estimator into the
functional. The resulting plug-in estimators typically converge
faster than the function estimators; in certain cases one even
obtains root n consistent and efficient estimators. The method can,
in particular, be applied to regression models with independent
errors and covariates: By making use of the convolution
representation one can, for example, construct root n consistent and
efficient estimators for densities and conditional expectations.
An important application of the plug-in method is the estimation of
the error variance and, more generally, of linear functionals of the
error distribution in nonparametric regression. We show that the
residual-based empirical estimator is efficient. In particular, it
remains efficient if the assumption of independence between errors
and covariates is not justified.This talk is based on joint work with Anton Schick and Wolfgang
Wefelmeyer.