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arXiv · 1503.02163

Uniform Estimation Beyond the Mean

Andreas Maurer
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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.

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Andreas Maurer. 2015-03-07. Uniform Estimation Beyond the Mean. https://arxiv.org/abs/1503.02163

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