Single-stage multiple-comparison procedure for quantiles and other parameters

We present a single-stage multiple-comparison procedure for comparing parameters of independent systems, where the parameters are not necessarily means or steady-state means. We assume that for each system, the parameter has an estimation process that satisfies a central limit theorem (CLT) and that we have a consistent variance-estimation process for the variance parameter appearing in the CLT. The procedure allows for unequal run lengths or sample sizes across systems, and also allows for unequal and unknown variance parameters across systems. The procedure is asymptotically valid as the run lengths or sample sizes of all system grow large. One setting the framework encompasses is comparing quantiles of independent populations. It also covers comparing means or other moments of independent populations, functions of means, and steady-state means of stochastic processes.