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  • © 2007

Concentration Inequalities and Model Selection

Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1896)

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XIV
  2. Introduction

    Pages 1-13
  3. Gaussian Processes

    Pages 53-82
  4. Maximal Inequalities

    Pages 183-199
  5. Statistical Learning

    Pages 279-318
  6. Back Matter

    Pages 319-341

About this book

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.

Keywords

  • 62J0
  • Information
  • Maxima
  • adaptive estimation
  • concentration inequalities
  • empirical processes
  • model selection
  • statistical learning
  • information and communication, circuits

Authors, Editors and Affiliations

  • Université Blaise Pascal (Clermont-Ferrand), Aubière Cedex, France

    Jean Picard

  • Département de Mathématique, Université de Paris-Sud, Orsay Cedex, France

    Pascal Massart

About the editor

Prof. Massart has received the bronze medal of the CNRS (in mathematics and theoretical physics) in 1988 and the COPPS Presidents’ award in 1998.

Bibliographic Information

Buying options

eBook
USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-48503-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 79.99
Price excludes VAT (USA)