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This article is cited in 2 scientific papers (total in 2 papers)
Short Communications
Estimates with asymptotically uniformly minimal $d$-risk
A. A. Zaikin Kazan (Volga Region) Federal University
Abstract:
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.
Received: 18.10.2016 Accepted: 20.03.2018
Citation:
A. A. Zaikin, “Estimates with asymptotically uniformly minimal $d$-risk”, Teor. Veroyatnost. i Primenen., 63:3 (2018), 609–618; Theory Probab. Appl., 63:3 (2019), 500–505
Linking options:
https://www.mathnet.ru/eng/tvp5193https://doi.org/10.4213/tvp5193 https://www.mathnet.ru/eng/tvp/v63/i3/p609
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Abstract page: | 277 | Full-text PDF : | 28 | References: | 33 | First page: | 9 |
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