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Biometrika 1971 58(1):227-228; doi:10.1093/biomet/58.1.227
© 1971 by Biometrika Trust
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MISCELLANEA

A generalization of a fundamental theorem of ranking and selection

PAUL N. SOMERVILLE

RCA International Service Corporation and Florida Institute of Technology

Assume there are k populations, each with identical known distribution functions, except possibly for the value of the unknown parameter ø in each. A general problem is that of selecting 8 populations such that at least c of them have values of the parameter ø which differ from the value of 6 for at least one of the b ‘best’ by an amount not more than d. A theorem is proved which simplifies the task of finding the infimum of the probability of correct selection for a wide class of multistage procedures.

Key Words: Decision theory • Sequential and multistage procedures


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