On the critical value behaviour of multiple decision procedures

In this paper we investigate the asymptotic critical value behaviour of cer tain multiple decision procedures as e.g. simultaneous confidence intervals and simultaneous as well as stepwise multiple test procedures. Supposing t hat n hypotheses or parameters of interest are under consideration we inves tigate the critical value behaviour when n increases. More specifically, we answer e.g. the question by which amount the lengths of confidence interva ls increase when an additional parameter is added to the statistical analys is. Furthermore, critical values of different multiple decision procedures as for instance step-down and step-up procedures will be compared. Some gen eral theoretic results are derived and applied for various distributions.