ASYMPTOTICALLY OPTIMAL PROCEDURES FOR SEQUENTIAL ADAPTIVE SELECTION OF THE BEST OF SEVERAL NORMAL MEANS

This chapter presents asymptotically optimal procedures for sequential adaptive selection of the best of several normal means. It is shown that for a sequential procedure based on elimination, if k, δ,{μi} and σ2 are fixed and P* →1, then there is a sharp asymptotic lower bound for the natural measure of efficiency. The chapter describes the class of elimination procedures with adaptive sampling, which do solve the selection problem. It also presents some Monte Carlo simulations to illustrate the potential savings in sample size that can be achieved by using fairly simple adaptive sampling rules.