Two-Stage Multiple-Comparison Procedures for Steady-State Simulations

Procedures for multiple comparisons with the best are investigated in the context of steady-state simulation, whereby a number k of different systems (stochastic processes) are compared based upon their (asymptotic) means μ _i ( i = 1,2, . . ., k). The variances of these (asymptotically stationary) processes are assumed to be unknown and possibly unequal. We consider the problem of constructing simultaneous confidence intervals for μ _j≠iμ _j ( i = 1,2, . . ., k), which is known as multiple comparisons with the best (MCB). Our intervals are constrained to contain 0, and so are called constrained MCB intervals. In particular, two-stage procedures for construction of absolute- and relative-width confidence intervals are presented. Their validity is addressed by showing that the confidence intervals cover the parameters with probability of at least some user-specified threshold value, as the confidence intervals' width parameter shrinks to 0. The general assumption about the processes is that they satisfy a functional central limit theorem. The simulation output analysis procedures are based on the method of standardized time series (the batch means method is a special case). The techniques developed here extend to other multiple-comparison procedures such as unconstrained MCB, multiple comparisons with a control, and all-pairwise comparisons. Although simulation is the context in this paper, the results naturally apply to (asymptotically) stationary time series.