  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.
