Skip to main content
SpringerLink
Log in

Some properties of the risk set in multiple decision problems

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ferguson, T. S. (1967).Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York.

    MATH  Google Scholar 

  2. Murakami, M. (1976). On the reduction to a complete class in multiple decision problems.Ann. Inst. Statist. Math.,28, A, 145–165.

    Article  MathSciNet  Google Scholar 

Download references

Authors
  1. Masakatsu Murakami
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The Institute of Statistical Mathematics

About this article

Cite this article

Murakami, M. Some properties of the risk set in multiple decision problems. Ann Inst Stat Math 35, 175–183 (1983). https://doi.org/10.1007/BF02480973

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02480973

Keywords

Search

Navigation