Inference for the Mean Difference in the Two-Sample Random Censorship Model

Inference for the mean difference in the two-sample random censorship model is an important problem in comparative survival and reliability test studies. This paper develops an adjusted empirical likelihood inference and a martingale-based bootstrap inference for the mean difference. A nonparametric version of Wilks' theorem for the adjusted empirical likelihood is derived, and the corresponding empirical likelihood confidence interval of the mean difference is constructed. Also, it is shown that the martingale-based bootstrap gives a correct first order asymptotic approximation of the corresponding estimator of the mean difference, which ensures that the martingale-based bootstrap confidence interval has asymptotically correct coverage probability. A simulation study is conducted to compare the adjusted empirical likelihood, the martingale-based bootstrap, and Efron's bootstrap in terms of coverage accuracies and average lengths of the confidence intervals. The simulation indicates that the proposed adjusted empirical likelihood and the martingale-based bootstrap confidence procedures are comparable, and both seem to outperform Efron's bootstrap procedure.