A Lower Confidence Bound on the Probability of a Correct Selection

Abstract

In the problem of selecting the best of k populations, a natural rule is to select the population corresponding to the largest sample value of an appropriate statistic. As a retrospective analysis, a conservative lower confidence bound on the probability of a correct selection is derived when the probability density function has the monotone likelihood ratio property under the location parameter setting. The result is applied to the normal populations with both known and unknown common variance. Tables to implement the confidence bound are provided.