2015/03/07 by Maurer, Andreas
#60G05 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1503.02163
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.