Science China Mathematics

, Volume 61, Issue 6, pp 1129–1138 | Cite as

Balanced augmented jackknife empirical likelihood for two sample U-statistics

  • Conghua Cheng
  • Yiming Liu
  • Zhi Liu
  • Wang Zhou


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.


jackknife empirical likelihood U-statistics ROC curves Balanced augmented empirical likelihood 


62G10 62F40 


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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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhaoqing UniversityZhaoqingChina
  2. 2.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore
  3. 3.Department of MathematicsUniversity of MacauMacauChina
  4. 4.Department of Statistics and Applied ProbabilityNational University of SingaporeSingaporeSingapore

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