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

Etsuo Miyaoka, Kazuo Noda

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1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)21-35
Number of pages15
Issue number1
Publication statusPublished - 1 Jul 2010



  • James-Stein type matrix estimator
  • Matrix normal distributions
  • Parameter matrix linear function
  • Quadratic matrix loss functions
  • The Stein problem
  • Unknown covariance matrix

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