Likelihood ratio procedures for subset selection and ranking problems
Jayanti Chotai · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 1979
This report deals with procedures for random-size subset selection fromk(> 2) given populations where the distribution of ir^(i = l, ..., k)has a density f^(x;0^). Let ••• -®[k] denote unknown values ofthe parameters, and let ^[i]» ***'ïï[k] denote the corresponding populations.First, we have considered the problem of selection for consider the/sprocedure that selects TT. if sup L(0;x) > c L(0;x), where L(*;x) is the1 e e u . - - - - -itotal likelihood function, where is the region m the parameter space foriA9= (0^, ..., 0^) having 0^ as the largest component, where 9 is the maximum likelihood estimate of 0 , and where c is a given constant with 0 1) best populations,thereby generalizing the results for t = 1. For this problem, we haveconsidered a) selection of a set whose elements consist of subsets of thegiven populations having t members, and requiring that the set of the t• » • • •best populations is included with probability at least P , b) selection ofa subset of the populations so as to include all the t best populationswith probability at least P'*, and c) selection of a subset of the populationssuch that TT[j ^ is included with probability at least P*, j=k-t+l,.•., k. In the final section, we have discussed the relation between thetheories of subset selection based on likelihood ratios and statistical inferenceunder order restrictions, and have considered the complete rankingproblem.