| 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 mi ( i 5 1,2, . . . , k). The variances of these (asymptot-ically
stationary) processes are assumed to be unknown and possibly unequal. We consider the
problem of constructing simultaneous confidence intervals for mi 2 max jÞi mj ( i 5 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.
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