Permutation procedures with censored data

This paper extends the permutation procedures for truncated data in Diaconis et al. (http://www-stat.stanford.edu/∼∼susan/.) to doubly censored data. As in Diaconis et al. (http://www-stat.stanford.edu/∼∼susan/.), the proposed procedure is based on samples from the conditional distribution of rank statistics which is uniformly distributed on a set of permutations. Subsequently, our procedure is applied to testing independence with bivariate censored data and estimating a regression coefficient with doubly censored data. Also, when estimating a regression coefficient with doubly censored data, simulation studies show that the proposed procedure is superior to that of Akritas et al. (J. Amer. Statist. Assoc. 90 (1995) 170).