  We demonstrate and discuss nonasymptotic bounds in probability for the cost
of a regression scheme with a general loss function from the perspective of the
Rademacher theory, and for the optimality with respect to the average
$L^{2}$-distance to the underlying conditional expectations of least squares
regression outcomes from the perspective of the Vapnik-Chervonenkis theory.
  The results follow from an analysis involving independent but possibly
nonstationary training samples and can be extended, in a manner that we explain
and illustrate, to relevant cases in which the training sample exhibits
dependence.
