Smoothed empirical likelihood inference for the difference of two quantiles with right censoring

• We study the difference of quantiles in the two independent samples.
• A limiting distribution of the empirical log-likelihood ratio is a chi-squared distribution.
• We compare the empirical likelihood and the normal approximation methods.
• A real data illustrates empirical likelihood confidence bands using bootstrap method.

In this paper, using a smoothed empirical likelihood method, we investigate the difference of quantiles in the two independent samples and construct the confidence intervals. We prove that the limiting distribution of the empirical log-likelihood ratio is a chi-squared distribution like Shen and He (2007). In the simulation studies, in terms of coverage accuracy and average length of confidence intervals, we compare the empirical likelihood and the normal approximation methods with the optimal bandwidth selected by cross-validation. The empirical likelihood method has a better performance most of the time. Finally, a real clinical trial data is used to illustrate how to generate empirical likelihood confidence bands using bootstrap method.