Skip to main content
SpringerLink
Log in

Optimal construction of a selection of a subpopulation

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

Summary

The problem of selecting a subpopulation from a given populationII is to be, on the basis of measurements of members ofII, achieved by choosing those members ofII who satisfy the standards determined by a given selection cirterion and rejecting those who do not.

Since the optimum selection depends on the unknown parameter of the probability distribution ofII, it is here considered how to construct a decision function from the space of subsidiary sample having infor-mation on θ to the space of selections. Thus the existence of Bayes and minimax decision functions under the constraint defined by the selection criterion is proved. A necessary and sufficient condition for a decision function satisfying the constraint to be a Bayes decision function is also obtained.

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. Brinbaum, Z. W. and Chapman, D. G. (1950). On optimum selections from multinormal populations,Ann. Math. Statist.,21, 443–447.

    Article  MathSciNet  Google Scholar 

  2. Bourbaki, N. (1965). Éléments de mathematique,Topologie générale, Chapitre let 2, Hermann, Paris.

    MATH  Google Scholar 

  3. Chochran, W. G. (1951). Improvement by means of selection,Proc. Second Berkeley Sympo. on Math. Statist. and Probability, 449–470.

  4. Ferguson, T. S. (1967).Mathematical Statistics, Academic Press, New York.

    MATH  Google Scholar 

  5. Isii, K. (1967). The Lagrange multiplier method and admissibility,Surikagaku-Kokyu-roku,27, 73–87 (in Japanese).

    Google Scholar 

  6. Köthe, G. (1966)Topological Vector Space I, Translated by D. J. H. Garling, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  7. Lehmann, E. L. (1959).Testing Statistical Hypotheses, John Wiley and Sons, New York.

    MATH  Google Scholar 

  8. Noda, K. and Taga, Y. (1971). Minimax estimation method for the optimum decomposition of a sample space based on prior information,Ann. Inst. Statist. Math.,23, 1–29.

    Article  MathSciNet  Google Scholar 

  9. Noda, K. (1980). Bayes decision functions for selections of subpopulations, Recent Development in Statistical Inference and Data Analysis,Proc. Inter. Conference in Statist., in Tokyo, (ed. Matusita, K.), North-Holland Publishing Company, 227–236.

  10. Raj, D. (1954). On optimum selections from multivariate populations,Sankhyà,14, 363–366.

    MathSciNet  Google Scholar 

  11. Schwartz, L. (1967).Cours d'analyse I, Hermann, Paris.

    Google Scholar 

  12. Tiao, G. C. and Zellner, A. (1964). Bayes's theorem and the use of prior knowledge in regression analysis,Biometrika,51, 219–230.

    Article  MathSciNet  Google Scholar 

Download references

Authors
  1. Kazuo Noda
    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

Noda, K. Optimal construction of a selection of a subpopulation. Ann Inst Stat Math 37, 415–435 (1985). https://doi.org/10.1007/BF02481110

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02481110

Key words

Search

Navigation