Geodesic
On a non-parametric analogue of the information matrix
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 759-774 
Yu. A. Koševnik; B. Ya. Levit. On a non-parametric analogue of the information matrix. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 759-774. http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a5/
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     author = {Yu. A. Ko\v{s}evnik and B. Ya. Levit},
     title = {On a~non-parametric analogue of the information matrix},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {759--774},
     year = {1976},
     volume = {21},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a class of differentiable functions $\Phi(F)$ of distributions $F$, an analogue of the information matrix $I(F)$ is considered. In terms of matrix $I(F)$, bounds for risks in estimating $\Phi(F)$ are obtained; this is an extension, to the non-parametric case, of a result of J. Hajek [2]. Some examples are discussed including estimation of $\Phi(F)$ under the restriction that the values of differentiable functions $\Psi(F)$ are known.