Some properties of the risk set in multiple decision problems

  • Masakatsu Murakami


Some properties of the risk set of a decision problem withn-action,m-sample and 2-parameter are considered. It is shown that the number of vertices of the risk set is equal tomn−(t 1+t 2), and that the number of essentially nonrandomized decision rules (defined in Section 1) in the minimal complete class is equal tom(n−1)+1−t 1, wheret 1 andt 2 are defined in Section 2. Also, a procedure is given for getting all nonrandomized decision rules in the minimal complete class.


Decision Rule Decision Problem Action Space Coordinate Form Complete Class 
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  1. [1]
    Ferguson, T. S. (1967).Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York.Google Scholar
  2. [2]
    Murakami, M. (1976). On the reduction to a complete class in multiple decision problems.Ann. Inst. Statist. Math.,28, A, 145–165.MATHMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1983

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  • Masakatsu Murakami

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