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Cram\'er type moderate deviations for two-sample Studentized \(U\)-statistics with applications

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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 Cram\'er 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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      Journal
      2014-07-16
      2015-11-13
      1407.4546

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

      Custom metadata
      62E17, 60F10, 62G10, 62F40
      math.ST math.PR stat.TH

      Probability, Statistics theory

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