Concentration Inequalities and Model Selection: Ecole d’Ete de Probabilites de Saint-Flour XXXIII – 2003

Pascal Massart, Jean Picard (editor)3540484973, 9783540484974, 9783540485032

Since the impressive works of Talagrand, concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn out to be essential tools to develop a non-asymptotic theory in statistics, exactly as the central limit theorem and large deviations are known to play a central part in the asymptotic theory. An overview of a non-asymptotic theory for model selection is given here and some selected applications to variable selection, change points detection and statistical learning are discussed. This volume reflects the content of the course given by P. Massart in St. Flour in 2003. It is mostly self-contained and accessible to graduate students.

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Table of contents :
Front Matter….Pages I-XIV
Introduction….Pages 1-13
Exponential and Information Inequalities….Pages 15-51
Gaussian Processes….Pages 53-82
Gaussian Model Selection….Pages 83-146
Concentration Inequalities….Pages 147-181
Maximal Inequalities….Pages 183-199
Density Estimation via Model Selection….Pages 201-277
Statistical Learning….Pages 279-318
Back Matter….Pages 319-341