Normal approximation for nonlinear statistics using a concentration inequality approach
Statistics Theory
2009-09-29 v1 Statistics Theory
Abstract
Let be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds for are obtained. The bounds are the best possible for many known statistics. Applications to U-statistics, multisample U-statistics, L-statistics, random sums and functions of nonlinear statistics are discussed.
Cite
@article{arxiv.0708.4272,
title = {Normal approximation for nonlinear statistics using a concentration inequality approach},
author = {Louis H. Y. Chen and Qi-Man Shao},
journal= {arXiv preprint arXiv:0708.4272},
year = {2009}
}
Comments
Published at http://dx.doi.org/10.3150/07-BEJ5164 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)