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Necessary conditions for admissibility of matrix linear estimators in a multivariate linear model

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Abstract

This article provides necessary conditions for the admissibility of matrix linear estimators of an estimable parameter matrix linear function under two kinds of quadratic matrix loss functions in a multivariate linear model following a family of matrix normal distributions, where the covariance matrix associated is completely unknown. Further it is demonstrated that if a more concrete condition supplied for one of the subdivided conditions is satisfied, then the special condition concerning the Stein problem is necessary for the admissibility of the kind of estimators under each of the loss functions.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, Japan

    Etsuo Miyaoka & Kazuo Noda

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  1. Etsuo Miyaoka
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  2. Kazuo Noda
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Correspondence to Etsuo Miyaoka.

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Miyaoka, E., Noda, K. Necessary conditions for admissibility of matrix linear estimators in a multivariate linear model. Metrika 72, 21–35 (2010). https://doi.org/10.1007/s00184-009-0238-3

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  • DOI: https://doi.org/10.1007/s00184-009-0238-3

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