Geodesic
On a class ol nonparametric estimates of nonlinear functionals of a density
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 2, pp. 404-409 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new class of nonparametric estimated of functionals of the type $J=\int F(g(x))\,dx$ (where $F(\,\cdot\,)$ is a certain function and $g(x)$ is the unknown density function) is proposed. The estimates are based on combination of Rosenblatt–Parzen's estimate of the density and Hoeffing's $U$-statistic. They are called quasi-$U$-statistics. The performance of quasi-$U$-statistics is demonstrated by an example of estimation of the squared density integral. 
@article{TVP_1974_19_2_a15,
     author = {Yu. G. Dmitriev and F. P. Tarasenko},
     title = {On a~class ol nonparametric estimates of nonlinear functionals of a~density},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {404--409},
     year = {1974},
     volume = {19},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_2_a15/}
}
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Yu. G. Dmitriev; F. P. Tarasenko. On a class ol nonparametric estimates of nonlinear functionals of a density. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 2, pp. 404-409. http://geodesic.mathdoc.fr/item/TVP_1974_19_2_a15/