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arXiv · 1407.4546

Cramér-type moderate deviations for Studentized two-sample $U$-statistics with applications

Jinyuan Chang·Qi-Man Shao·Wen-Xin Zhou
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Abstract

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. 2016-09-28. Cramér-type moderate deviations for Studentized two-sample $U$-statistics with applications. https://doi.org/10.1214/15-aos1375

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