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2009 General oracle inequalities for model selection
Charles Mitchell, Sara van de Geer
Electron. J. Statist. 3: 176-204 (2009). DOI: 10.1214/08-EJS254

Abstract

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 and prove them at a very general level, for general margin and power tail behavior of the excess losses. These bounds we then apply to typical examples.

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Charles Mitchell. Sara van de Geer. "General oracle inequalities for model selection." Electron. J. Statist. 3 176 - 204, 2009. https://doi.org/10.1214/08-EJS254

Information

Published: 2009
First available in Project Euclid: 3 March 2009

zbMATH: 1326.62076
MathSciNet: MR2485876
Digital Object Identifier: 10.1214/08-EJS254

Subjects:
Primary: 62G05
Secondary: 62G20

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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