Summary
The selection oft out ofk populations with parameters θi (i=1, ...,k) is said to result in an ψ-correct decision provided ψ (minimum selected θ)>maximum non-selected θ where ψ(θ) (>θ) is an increasing function. For the cases of location or scale parameters the minimum probability of ψ-correct decision over the entire parameter space is shown to be no less than the minimum probability of correct selection over a preference zone determined by ψ(θ). For other types of parameters this result is shown to be true under certain conditions linking the distribution function and the ψ function.
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References
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Bofinger, E. ψ-correct decision for selection and elimination. Ann Inst Stat Math 38, 445–450 (1986). https://doi.org/10.1007/BF02482531
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DOI: https://doi.org/10.1007/BF02482531