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Finite sample bounds on the estimation error of the mean by the empiricalmean, uniform over a class of functions, can often be conveniently obtained interms of Rademacher or Gaussian averages of the class. If a function of nvariables has suitably bounded partial derivatives, it can be substituted forthe empirical mean, with uniform estimation again controlled by Gaussianaverages. Up to a constant the result recovers standard results for theempirical mean and more recent ones about U-statistics, and extends to ageneral class of estimation problems.

Uniform Estimation Beyond the Mean