Conditional studentized survival tests for randomly censored models Running headline: Studentized survival tests

It is shown that in the case of heterogenous censoring distributions studentized survival tests can be carried out as conditional permutation tests given the order statistics and their censoring status. The result is based on a conditional central limit theorem for permutation statistics. It holds as well for linear test statistics as for sup-statistics. The procedure works under one of the following general circumstances for the two-sample problem: the unbalanced sample size case, higly censored data, certain non-convergent weight functions or under alternatives. For instance the two-sample log rank test can be asymptotically carried out as a conditional test if the relative amount of uncensored observations vanishes asymptotically as long as the number of uncensored observations becomes innnite. Similar results hold whenever the sample sizes n 1 and n 2 are unbalanced in the sense that n 1 =n 2 ! 0 and n 1 ! 1 hold.