On selecting the best component of a multivariate normal population

The problem of selecting the component having the largest population mean in a k-variate normal population is discussed when all the means, variances and correlations are unknown. The indifference-zone formulation has been adopted, and we propose a two-stage procedure (PS) that guarantees the nominal value (P∗) of probability of correct selection under the assumption that all the correlations are non-negative. The procedure PS is the only method thus far proposed that will accomplish the desired objective. It is also of some interest that PS is asymptotically (as δ∗ ↛ 0) "better" than the procedure PR of Dudewicz and Dalal (1975) for k = 2, P∗≤.95, while for k≥3 the procedure PR is "better" than PS when ρij = 0, i≠j. This comparison is naturally valid when both PR and PS are applicable, and of course there are situations where only PS is applicable.