On the estimation of the true probability of a correct selection

Abstract

For ranking and selection problems, the true probabiIity of a correct selection P(CS) is unknown even if a selection is made under the indifference-zone approach. Thus to estimate the true P(CS) some Bayes estimators and a bootstrap estimator are proposed for two normcal populations with common known variance. Also a bootstrap estimator and a bootstrap confidence interval are proposed for normal populations with common unknown variance. Some comparisons between proposed estimators and some other known estimators are made via Monte Carlo simulations.

Keywords:

• Indifference-zone
• correct selection
• Bayes estimators
• HPD credible sets
• bootstrap estimators
• bootstrap confidence intervals