  Model selection is often performed by empirical risk minimization. The
quality of selection in a given situation can be assessed by risk bounds, which
require assumptions both on the margin and the tails of the losses used.
Starting with examples from the 3 basic estimation problems, regression,
classification and density estimation, we formulate risk bounds for empirical
risk minimization under successively weakening conditions and prove them at a
very general level, for general margin and power tail behavior of the excess
losses.
