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Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 3, Pages 609–618 (Mi tvp5193)  

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.

DOI: https://doi.org/10.4213/tvp5193

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English version:
Theory of Probability and its Applications, 2019, 63:3, 500–505

Bibliographic databases:

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

Citation in format AMSBIB
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