Geodesic
On estimation of functionals of the probability density function and its derivatives
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 662-668 
Yu. G. Dmitriev; F. P. Tarasenko. On estimation of functionals of the probability density function and its derivatives. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 662-668. http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a26/
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     title = {On estimation of functionals of the probability density function and its derivatives},
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     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a26/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For functionals of the type $I=\int_{-\infty}^\infty H(f(y)),f'(y),\dots,f^{(r)}(y))\,dy$ the estimates $I_N=\int_{-k_N}^{k_N}H(f_N(y),\dots,f_N^{(r)}(y))\,dy$ are considered. Here $f_N(y),\dots,f_N^{(r)}(y)$ are nonparametric estimates of the density and of its derivatives introduced by Rosenblatt and studied by Parzen, Bhattacharya, Nadaraya and others. Theorems on convergence of the estimates with probability one are proved for Fisher's information, the entropy and the integral of the squared density. Convergence in probability are also investigated.