Statistics : Ranking and Selection Problems

About fifty years ago statistical inference problems were first formulated in the now-familiar "Ranking and Selection" framework. Ranking and selection problems broadly deal with the goal of ordering of different populations in terms of unknown parameters associated with them. We deal with the following aspects of Ranking and Selection Problems:

• Obtaining optimal ranking and selection procedures using decision theoretic approach;
• Obtaining optimal ranking and selection procedures under heteroscedasticity;
• Simultaneous confidence intervals for all distances from the best and/or worst populations, where the best (worst) population is the one corresponding to the largest (smallest) value of the parameter;
• Estimation of ranked parameters when the ranking between parameters is not known apriori;
• Estimation of (random) parameters of the populations selected using a given decision rule for ranking and selection problems.