Acta Applicandae Mathematica

, Volume 43, Issue 1, pp 87–95 | Cite as

A subclass of bayes linear estimators that are minimax

  • Kurt Hoffmann


In the linear regression model with ellipsoidal parameter constraints, the problem of estimating the unknown parameter vector is studied. A well-described subclass of Bayes linear estimators is proposed in the paper. It is shown that for each member of this subclass, a generalized quadratic risk function exists so that the estimator is minimax. Moreover, some of the proposed Bayes linear estimators are admissible with respect to all possible generalized quadratic risks. Also, a necessary and sufficient condition is given to ensure that the considered Bayes linear estimator improves the least squares estimator over the whole ellipsoid whatever generalized risk function is chosen.

Mathematics Subject Classifications (1991)

primary: 62J05 secondary: 62C10 62C20 

Key words

linear regression Bayes linear estimation restricted parameter space minimax property 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Kurt Hoffmann
    • 1
  1. 1.Ludwig-Renn-Strasse 37BerlinGermany

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