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Concentration Inequalities and Model Selection

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

  • Pascal Massart
  • Jean Picard

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

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Pages 1-13
  3. Pages 53-82
  4. Pages 183-199
  5. Pages 279-318
  6. Back Matter
    Pages 319-341

About this book

Introduction

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

Authors and affiliations

  • Pascal Massart
    • 1
  1. 1.Département de MathématiqueUniversité de Paris-SudOrsay CedexFrance

Editors and affiliations

  • Jean Picard
    • 1
  1. 1.Université Blaise Pascal (Clermont-Ferrand)Aubière CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-48503-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-48497-4
  • Online ISBN 978-3-540-48503-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site