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      Cram\'er type moderate deviation theorems for self-normalized processes

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          Abstract

          Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new randomized concentration inequality and establish a Cram\'er type moderate deviation theorem for general self-normalized processes which include many well-known Studentized nonlinear statistics. In particular, a sharp moderate deviation theorem under optimal moment conditions is established for Studentized \(U\)-statistics.

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          Author and article information

          Journal
          2014-05-06
          2014-08-16
          Article
          1405.1218
          611f3dc4-170a-40ba-8bcb-07be47c9b9dc

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

          History
          Custom metadata
          60F05, 60F10
          52 pages, Old title of an earlier version: Cram\'er type moderate deviation theorems for Studentized non-linear statistics
          math.PR math.ST stat.TH

          Probability,Statistics theory
          Probability, Statistics theory

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