Optimal oracle inequalities for model selection

Details Optimal oracle inequalities for model selection Optimal oracle inequalities for model selection

2008-06-25

arxiv.org/abs/0806.4140v1

Mathematics

Statistics Theory

Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics

Scientific paper

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.

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