English

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.

Keywords

Cite

@article{arxiv.1503.02163,
  title  = {Uniform Estimation Beyond the Mean},
  author = {Andreas Maurer},
  journal= {arXiv preprint arXiv:1503.02163},
  year   = {2015}
}
R2 v1 2026-06-22T08:46:36.992Z