On testing equality of two censored samples

This paper examines some stochastic processes derived from rank related statistics for testing equality of distributions of two samples with possibly censored data. Based on the martingale approach, the null distributions of these processes are approximated through simulating zero-mean Gaussian processes. Each observed process can then be compared with a large number of realizations from the corresponding Gaussian process. Based on these comparisons, a supremum test is discussed to assess equality of two censored samples. The proposed methods are illustrated in two applications.