This thesis proposed two nonparametric statistical tests, based on the Kolmogorov-Smirnov distance and L2 mallows disatnce. To implement the proposed tests, nonparametric bootstrap method is employed to approximate the distributions of the test statistics to construct the corresponding bootstrap confidence interval procedures. Monte-Carlo simulations are performed to investigate the actual type I error of the proposed bootstrap procedures. It is found that the type I error of the bootstrap BC confidence interval procedure is close to the nominal level when censoring is not heavy and the boosttrap percentile confidence interval procedure works well when Kolmogorov-Smirnov distance is used to characterize the equivalence. When the data is heavily censored, the procedures based on the Kolmogorov-Smirnov distance have very conservative type I errors, while the procedures based on the Mallows distance are very liberal. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2007-08-01 10:43:32.345