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October 2016 Cramér-type moderate deviations for Studentized two-sample $U$-statistics with applications
Jinyuan Chang, Qi-Man Shao, Wen-Xin Zhou
Ann. Statist. 44(5): 1931-1956 (October 2016). DOI: 10.1214/15-AOS1375


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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Jinyuan Chang. Qi-Man Shao. Wen-Xin Zhou. "Cramér-type moderate deviations for Studentized two-sample $U$-statistics with applications." Ann. Statist. 44 (5) 1931 - 1956, October 2016.


Received: 1 June 2015; Published: October 2016
First available in Project Euclid: 12 September 2016

zbMATH: 1272.68116
MathSciNet: MR3546439
Digital Object Identifier: 10.1214/15-AOS1375

Primary: 60F10, 62E17
Secondary: 62E20, 62F40, 62H15

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 5 • October 2016
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