  In this paper, we propose a procedure to test the independence of bivariate
censored data, which is generic and applicable to any censoring types in the
literature. To test the hypothesis, we consider a rank-based statistic,
Kendall's tau statistic. The censored data defines a restricted permutation
space of all possible ranks of the observations. We propose the statistic, the
average of Kendall's tau over the ranks in the restricted permutation space. To
evaluate the statistic and its reference distribution, we develop a Markov
chain Monte Carlo (MCMC) procedure to obtain uniform samples on the restricted
permutation space and numerically approximate the null distribution of the
averaged Kendall's tau. We apply the procedure to three real data examples with
different censoring types, and compare the results with those by existing
methods. We conclude the paper with some additional discussions not given in
the main body of the paper.
