Geodesic
On efficient estimation of smooth functionals
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 199-205

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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.
Keywords: independent observations, a “plug-in” estimator, a kernel estimator, a locally asymptotically minimax estimator, a smooth functional, asymptotic efficiency. 
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     author = {L. Goldstein and R. Khas'minskii},
     title = {On efficient estimation of smooth functionals},
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     year = {1995},
     language = {en},
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L. Goldstein; R. Khas'minskii. On efficient estimation of smooth functionals. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 199-205. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a16/