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The least favorable configuration of a two-stage procedure for selecting the largest normal mean. (English) Zbl 0827.62022

Hoppe, Fred M. (ed.), Multiple comparisons, selection, and applications in biometry. A Festschrift in honor of Charles W. Dunnett. New York, NY: Marcel Dekker. Stat., Textb. Monogr. 134, 247-265 (1993).
Summary: The first author and M. B. Heffernan [J. Stat. Plann. Inference 31, No. 2, 147-168 (1992; Zbl 0759.62013)] introduced a two-stage procedure for selecting the normal population with the largest mean when all the populations have a common known variance. In their procedure, a random number of populations are allowed to enter the second stage; this number is controlled by an experimenter-specified upper bound. They consider the determination of sample sizes and constants needed to implement the selection procedure, and they conjecture that the infimum of the probability of correct selection over configurations of population means \(\underline {\mu}= (\mu_1, \dots, \mu_k)\) for which \(\mu_{[ k]}- \mu_{[k- 1]}\geq \delta^*\) occurs when \(\mu_{[1 ]}= \mu_{[k -1]}= \mu_{[k ]}- \delta^*\), where \(\delta^*\) is a given positive number and \(\mu_{[1 ]}\leq \dots\leq \mu_{[k ]}\) are the ordered population means.
Their conjecture is proved in this paper. Some extensions of this two- stage rule and this result are discussed.
For the entire collection see [Zbl 0816.00044].

MSC:

62F07 Statistical ranking and selection procedures

Citations:

Zbl 0759.62013
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