The present paper derives various survival tests and their optimality results for randomly censored lifetime data by an extension of familiar rank tests arguments. The approach is based on local asymptotic normal models which have a natural interpretation in terms of hazard rates. In particular, the description of classical rank tests by hazard rates may be of separate interest. As an application of the new methods, a justification of conditional survival tests is given also under unequal censoring distributions. It turns out that censoring is a nuisance phenomenon which asymptotically drops out. Conditional tests are exact permutation tests which are shown to be equivalent to their unconditional counterparts. They have all kinds of optimality properties and can be recommended for applications at least in those cases when a model with equal censorship cannot be excluded under the null hypothesis.
"Conditional Rank Tests for Randomly Censored Data." Ann. Statist. 19 (3) 1434 - 1456, September, 1991. https://doi.org/10.1214/aos/1176348255