In this paper, we investigate the two sample U-statistics by jackknife empirical likelihood (JEL), a versatile nonparametric approach. More precisely, we propose the method of balanced augmented jackknife empirical likelihood (BAJEL) by adding two articial points to the original pseudo-value dataset, and we prove that the log likelihood ratio based on the expanded dataset tends to the χ2 distribution.
This work was supported by the Natural Science Foundation of Guangdong Province (Grant No. 2016A030307019), the Higher Education Colleges and Universities Innovation Strong School Project of Guangdong Province (Grant No. 2016KTSCX153), Science and Technology Development Fund of Macau (Grant No. 127/2016/A3), National Natural Science Foundation of China (Grant No. 11401607) and a grant at the National University of Singapore (Grant No. R-155-000-181-114). The authors are grateful to two anonymous referees for comments and suggestions that led to substantial improvements in the paper.
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