On efficient estimation of smooth functionals

The problem of the estimation of smooth functionals $\Lambda$ defined on a set of densities $\mathcal{F}$ is considered. A simple “plug-in” estimator $\Lambda(\widehat f_n)$ 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.