Convergence Results for Sequential Estimation of the Largest Mean.

We consider the sequential estimation of the largest mean of k populations when the observations are normally distributed with a common unknown variance and the goal is to control the mean square error MSE at a prespecified level. By eliminating from the experiment populations which the data indicate are not associated with the largest mean, it is shown that, compared to existing procedures, significant savings in sample size can be obtained. Weak convergence results are obtained for the stopping times and the estimate of the largest mean as consequences of more general results these are used to compute the asymptotic MSE.