Open Access
November 2016 Cramér type moderate deviation theorems for self-normalized processes
Qi-Man Shao, Wen-Xin Zhou
Bernoulli 22(4): 2029-2079 (November 2016). DOI: 10.3150/15-BEJ719


Cramér 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 Cramér 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.


Download Citation

Qi-Man Shao. Wen-Xin Zhou. "Cramér type moderate deviation theorems for self-normalized processes." Bernoulli 22 (4) 2029 - 2079, November 2016.


Received: 1 September 2013; Revised: 1 August 2014; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1272.68116
MathSciNet: MR3498022
Digital Object Identifier: 10.3150/15-BEJ719

Keywords: $U$-statistics , Moderate deviation , nonlinear statistics , relative error , self-normalized processes , Studentized statistics

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 4 • November 2016
Back to Top