Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 2, pp. 404-409
Citer cet article
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/
@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/}
}
TY - JOUR
AU - Yu. G. Dmitriev
AU - F. P. Tarasenko
TI - On a class ol nonparametric estimates of nonlinear functionals of a density
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1974
SP - 404
EP - 409
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_2_a15/
LA - ru
ID - TVP_1974_19_2_a15
ER -
%0 Journal Article
%A Yu. G. Dmitriev
%A F. P. Tarasenko
%T On a class ol nonparametric estimates of nonlinear functionals of a density
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1974
%P 404-409
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1974_19_2_a15/
%G ru
%F TVP_1974_19_2_a15
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.
