Date of Award


Degree Type

Closed Thesis

Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Dr. Yichuan Zhao - Chair

Second Advisor

Dr. Jiawei Liu

Third Advisor

Dr. Xu Zhang

Fourth Advisor

Dr. Yu-Sheng Hsu


In this thesis, we study two independent samples under right censoring. Using a smoothed empirical likelihood method, we investigate the difference of quantiles in the two samples and construct the pointwise confidence intervals from it as well. The empirical log-likelihood ratio is proposed and its asymptotic limit is shown as a chi-squared distribution. In the simulation studies, in terms of coverage accuracy and average length of confidence intervals, we compare the empirical likelihood and the normal approximation method. It is concluded that the empirical likelihood method has a better performance. At last, a real clinical trial data is used for the purpose of illustration. Numerical examples to illustrate the efficacy of the method are presented.