Cram\'er type moderate deviation theorems for self-normalized processes
Probability
2016-06-07 v5 Statistics Theory
Statistics Theory
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 -statistics.
Cite
@article{arxiv.1405.1218,
title = {Cram\'er type moderate deviation theorems for self-normalized processes},
author = {Qi-Man Shao and Wen-Xin Zhou},
journal= {arXiv preprint arXiv:1405.1218},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.3150/15-BEJ719 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)