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The Notion of Asymptotically Least Favorable Configuration in Selection and Ranking Problems

In: Probability and Statistical Inference

Author

Listed:
  • Jaroslav Hustý

    (Academy of Sciences, Mathematical Institute of Czechoslovak)

Abstract

In the indifference zone approach to problems of selection and ranking of populations, a crucial role is played by the least favorable configuration (LFC) of parameters. In those cases when LFC does not exist or could not be found, the concept of asymptotically least favorable configuration (ALFC) has been used rather vaguely. In this paper a possible proper definition of ALFC is given and it is shown that under very slight and natural conditions “asymptotically” means either for the sample size tending to infinity or equivalently for the preference zone tending to the whole parameter set. These problems are treated for k populations in two different cases: 1. indifference zone being part of a k-dimensional parameter set (e. g. when selecting the best t from k populations) and 2. indifference zone being part of a onedimensional parameter set (when selecting populations better than a control).

Suggested Citation

  • Jaroslav Hustý, 1982. "The Notion of Asymptotically Least Favorable Configuration in Selection and Ranking Problems," Springer Books, in: Wilfried Grossmann & Georg Ch. Pflug & Wolfgang Wertz (ed.), Probability and Statistical Inference, pages 143-155, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-7840-9_14
    DOI: 10.1007/978-94-009-7840-9_14
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