Skip to main content

Part of the book series: Lecture Notes in Statistics ((LNS,volume 6))

  • 162 Accesses

Abstract

In this chapter, we shall discuss the modified principles of minimax criteria (such as г-minimax and restricted minimax) for multiple decision problems.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berger, R. L. (1977). Minimax subset selection for loss measured by subset size. Mimeo. Ser. #489, Dept. of Statist., Purdue Univ.

    Google Scholar 

  2. Berger, R. L. and Gupta, S. S. (1980). Minimax subset selection rules with applications to unequal variance (unequal sample size) problems. Scand. J. Statist. 7, 21–26.

    MathSciNet  MATH  Google Scholar 

  3. Bjørnstad, J. (1980). A class of Schur-procedures and minimax theory for subset selection. To appear in Ann. Statist.

    Google Scholar 

  4. Brown, L. D., Cohen, A. and Strawderman, W. E. (1976). A complete class of theorem for strict monotone likelihood ratio with applications. Ann. Statist. 4, 712–722.

    Article  MathSciNet  MATH  Google Scholar 

  5. Deely, J. J. and Gupta, S. S. (1968). On the properties of subset selection properties of subset selection procedures. Sankhyā Ser. A, 30, 37–50.

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  7. Gupta, S. S. (1965). On multiple decision (selecting and ranking) rules. Technometrics 7, 225–245.

    Article  MATH  Google Scholar 

  8. Gupta, S. S. and Hsu, J. C (1978). On the performance of some subset selection procedures. Comm. Statist. B7, 561–591.

    Google Scholar 

  9. Gupta, S. S. and Huang, D. Y. (1976). Subset selection procedure for the means and variances of normal populations: unequal sample sizes case. Sankhyā Ser. B, 38, 112–128.

    MathSciNet  MATH  Google Scholar 

  10. Gupta, S. S. and Huang, D. Y. (1977). On some Γ-minimax selection and multiple comparison procedures. Statistical Decision Theory and Related Topics II (Ed. Gupta, S. S. and Moore, D. S.), 139–155.

    Google Scholar 

  11. Gupta, S. S. and Huang, D. Y. (1980a). A note on optimal subset selection procedures. To appear in Ann. Statist.

    Google Scholar 

  12. Gupta, S. S. and Huang, D. Y. (1980b). An essentially complete class of multiple decision procedures. To appear in Journal of Statistical Planning and Inference.

    Google Scholar 

  13. Gupta, S. S. and Miescke, K. J. (1978). Optimality of subset selection procedure for ranking means of three normal populations. Mimeo. Ser. #78–19, Dept. of Statist., Purdue Univ., Lafayette, IN 47907.

    Google Scholar 

  14. Gupta, S. S., Nagel K. and Panchapakesan, S. (1973). On the order statistics from equally correlated normal variables. Biometrika 60, 403–413.

    Article  MathSciNet  MATH  Google Scholar 

  15. Karlin, S. and Rubin, H. (1956). The theory of decision procedures for distributions with monotone likelihood ratio. Ann. Math. Statist. 27, 272–299.

    Article  MathSciNet  MATH  Google Scholar 

  16. Lehmann, E. L. (1961). Some model I problems of selection. Ann. Math. Statist. 32, 990–1012.

    Article  MathSciNet  MATH  Google Scholar 

  17. Miescke, K. J. (1979). r-minimax selection procedures in simultaneous testing problems. Mimeo. Ser. #79–1, Dept. of Statist., Purdue Univ., IN 47907.

    Google Scholar 

  18. Nagel, K. (1970). On subset selection rules with certain optimality properties. Mimeo. Ser. #222, Dept. of Statist., Purdue Univ., Lafayette, IN 47907.

    Google Scholar 

  19. Oosterhoff, J. (1969). Combination of One-Sided Statistical Tests. Mathematical Centre Tracts 28, Amsterdam.

    MATH  Google Scholar 

  20. Randies, R. H. and Hollander, M. (1971). r-minimax selection procedures in treatments versus control problems. Ann. Math. Statist. 42, 330–341.

    Article  MathSciNet  Google Scholar 

  21. Seal, K. C (1955). On a class of decision procedures for ranking means of normal populations. Ann. Math. Statist. 36, 387–397.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Gupta, S.S., Huang, DY. (1981). Modified Minimax Decision Procedures. In: Multiple Statistical Decision Theory: Recent Developments. Lecture Notes in Statistics, vol 6. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5925-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-5925-1_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90572-3

  • Online ISBN: 978-1-4612-5925-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics