  Many statistical estimation procedures lead to nonconvex optimization
problems. Algorithms to solve these are often guaranteed to output a stationary
point of the optimization problem. Oracle inequalities are an important
theoretical instrument to asses the statistical performance of an estimator.
Oracle results have focused on the theoretical properties of the uncomputable
(global) minimum or maximum. In the present work a general framework used for
convex optimization problems to derive oracle inequalities for stationary
points is extended. A main new ingredient of these oracle inequalities is that
they are sharp: they show closeness to the best approximation within the model
plus a remainder term. We apply this framework to different estimation
problems.
