On Efficient Estimation of Smooth Functionals

Abstract

The problem of the estimation of smooth functionals $\Lambda $ defined on a set of densities $\mathcal{F}$ is considered. A simple “plug-in” estimator $\Lambda (\hat f_n )$ is shown to be asymptotically efficient in the sense of Levit [5], [6], where $\hat f_n $ is an “undersmoothed” kernel estimate of the density f. The approach is compared to others in the literature.