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Open Access Publications from the University of California

Cramer-Type moderate deviations for studentized two-sample u-statistics with applications

  • Author(s): Chang, J
  • Shao, QM
  • Zhou, WX
  • et al.

© 2016 Institute of Mathematical Statistics. Two-sample U-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cramér-type moderate deviation theorems for Studentized two-sample U-statistics in a general framework, including the two-sample t-statistic and Studentized Mann-Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is established for the two-sample t-statistic. These results extend the applicability of the existing statistical methodologies from the one-sample t-statistic to more general nonlinear statistics. Applications to two-sample large-scale multiple testing problems with false discovery rate control and the regularized bootstrap method are also discussed.

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