Subset selection based on likelihood from uniform and related popupulations

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Abstract
Let πi (i=1,2,…, k) be charceterized by the uniform distribution on (ai;bi), where exactly one of ai and bi is unknown. With unequal sample sizes, suppose that from the k (>=2) given populations, we wish to select a random-size subset containing the one with the smllest value of θi= bi - ai. RuleRi selects π if a likelihood-based k-dimensional confidence region for the unknown (θ1,… θk) contains at least one point having θi as its smallest component. A second rule, R , is derived through a likelihood ratio and turns out to be that of Barr and prabhu whenthe sample sizes are equal. Numerical comparisons are made. The results apply to the larger class of densities g ( z ; θi) =M(z)Q(θi) if a(θi) < z i). Extensions to the cases when both ai and bi are unknown and when θj isof interest are indicated. 1<=j<=k

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