31
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Cram\'{e}r-type moderate deviations for Studentized two-sample \(U\)-statistics with applications

      Preprint

      Read this article at

          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          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\'{e}r-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.

          Related collections

          Author and article information

          Journal
          10.1214/15-AOS1375
          1407.4546
          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Probability,Statistics theory
          Probability, Statistics theory

          Comments

          Comment on this article