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Asymptotic risk behavior of mean vector and variance estimators and the problem of positive normal mean

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Abstract

Asymptotic risk behavior of estimators of the unknow variance and of the unknown mean vector in a multivariate normal distribution is considered for a general loss. It is shown that in both problems this characteristic is related to the risk in an estimation problem of a positive normal mean under quadratic loss function. A curious property of the Brewster-Zidek variance estimator of the normal variance is also noticed.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of Maryland, Baltimore County Campus, 21228-5398, Baltimore, MD, U.S.A.

    Andrew L. Rukhin

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  1. Andrew L. Rukhin
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Additional information

Research supported by NSF Grant DMS 9000999 and by Alexander von Humboldt Foundation Senior Distinguished Scientist Award.

University of Münster

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Rukhin, A.L. Asymptotic risk behavior of mean vector and variance estimators and the problem of positive normal mean. Ann Inst Stat Math 44, 299–311 (1992). https://doi.org/10.1007/BF00058642

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  • DOI: https://doi.org/10.1007/BF00058642

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