Academic

Consider an experiment in which p independent populations pi_i with corresponding unknown means theta_i are available, and suppose that for every 1< i < p, we can obtain a sample X_i1,…,X_in from pi_i. In this context, researchers are sometimes interested in selecting the populations that yield the largest sample means as a result of the experiment, and then estimate the corresponding population means theta_i. In this paper, we present a frequentist approach to the problem and discuss how to construct simultaneous confidence intervals for the means of the k selected populations, assuming that the populations pi_i are independent and normally distributed with a common variance sigma^2. The method, based on the minimization of the coverage probability, obtains confidence intervals that attain the nominal coverage probability for any p and k, taking into account the selection procedure.