Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Yichuan Zhao


In this thesis, we propose a smoothed empirical likelihood method for the difference of quantiles with paired samples. The empirical likelihood for the difference of two quantiles with independent samples has been studied by some researchers. However, for many vari- ables, we cannot ignore the correlation between the data. In this study, we construct two estimating equations for the difference of two quantiles and introduce a nuisance parameter in our proposed smoothed empirical likelihood. The limiting distribution of the smoothed empirical likelihood is the chi-square distribution. Simulation studies demonstrate that our method is valid for the difference of quantiles. We also apply the proposed method to a real data set to illustrate the interval estimate of the quantile difference of GDP between different years.


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