Uniform Estimation Beyond the Mean
Probability
2015-03-10 v1
Abstract
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has suitably bounded partial derivatives, it can be substituted for the empirical mean, with uniform estimation again controlled by Gaussian averages. Up to a constant the result recovers standard results for the empirical mean and more recent ones about U-statistics, and extends to a general class of estimation problems.
Cite
@article{arxiv.1503.02163,
title = {Uniform Estimation Beyond the Mean},
author = {Andreas Maurer},
journal= {arXiv preprint arXiv:1503.02163},
year = {2015}
}