Conditional studentized survival tests for randomly censored models

It is shown that in the case of heterogenous censoring distributions Studen tized survival tests can be carried out as conditional permutation tests gi ven the order statistics and their censoring status. The result is based on a conditional central limit theorem for permutation statistics. It holds f or linear test statistics as well as for sup-statistics, The procedure work s under one of the following general circumstances for the two-sample probl em: the unbalanced sample size case, highly censored data, certain non-conv ergent weight functions or under alternatives. For instance, the two-sample log rank test can be carried out asymptotically as a conditional test if t he relative amount of uncensored observations vanishes asymptotically as lo ng as the number of uncensored observations becomes infinite. Similar resul ts hold whenever the sample sizes n(1) and n(2) are unbalanced in the sense that n(1)/n(2) --> 0 and n(1) --> infinity hold.