Theory and Practice of Empirical Processes

  • Michel Talagrand
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 60)


In Chapter 9 we investigate how to control the supremum of the empirical process over a class of functions. The fundamental theoretical question in this direction is whether there exists a “best possible” method to control this supremum at a given size of the random sample. We offer a natural candidate for such a “best possible” method, in the spirit of the Bednorz-Latała result of Chapter 5. Whether this natural method is actually optimal is a major open problem. To illustrate that meditating on these theoretical questions might help to solve practical problems, we present a somewhat streamlined proofs of two deep recent results.


Empirical Process Invariant Probability Measure Admissible Sequence Spread Part Entropy Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Michel Talagrand
    • 1
  1. 1.Institut de MathématiquesUniversité Paris VIParis Cedex 05France

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