Geodesic
On a characteristic of the accuracy of estimating a~distribution density
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 425-431

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Within the framework of the scheme of independently observed random elements $X_1,\ldots,X_n$ with densities $p(x;\theta)$, $\theta\in\Theta$, the question is studied as to what extent is the possible asymptotic accuracy of the estimation related to the complex structure of the parameter set $\Theta$.
Keywords: estimation of a distribution density, asymptotic difficulty of an estimation problem, minimal risk, measure of complexity of the parameter set, Kolmogorov diameters. 
@article{TVP_1993_38_2_a11,
     author = {I. A. Ibragimov},
     title = {On a characteristic of the accuracy of estimating a~distribution density},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {425--431},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a11/}
}
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I. A. Ibragimov. On a characteristic of the accuracy of estimating a~distribution density. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 425-431. http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a11/