Estimates with asymptotically uniformly minimal $d$-risk
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 609-618
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The definition of a decision function with asymptotically ($n\to\infty$) uniformly minimal $d$-risk
is presented in the framework of the general theory of statistical inference.
Using this definition, we prove that the maximum likelihood estimate has asymptotically uniformly minimal $d$-risk.
This extends one result by
I. N. Volodin and A. A. Novikov [Theory Probab. Appl.,
38 (1994), pp. 118–128] for shrinking priors to the general class of continuous distributions. The proof uses the asymptotic representation of the posterior risk function, as obtained in
[A. A. Zaikin, J. Math. Sci. (N.Y.), 229 (2018), pp. 678–697].
Keywords:
$d$-risk, posterior risk asymptotics, maximum likelihood estimate.
@article{TVP_2018_63_3_a10,
author = {A. A. Zaikin},
title = {Estimates with asymptotically uniformly minimal $d$-risk},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {609--618},
publisher = {mathdoc},
volume = {63},
number = {3},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a10/}
}
A. A. Zaikin. Estimates with asymptotically uniformly minimal $d$-risk. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 609-618. http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a10/