Uniform Deviation Inequalities

  • Luc Devroye
  • Gábor Lugosi
Part of the Springer Series in Statistics book series (SSS)


This chapter is devoted to some basic inequalities that bound the maximal difference between probabilities and relative frequencies over a class of events. The bounds will be key tools in our study of density estimates. Let X 1,…,X n be i.i.d. random variables taking values in R d with common distribution
$$ \mu (A) = {\text{P}}\{ {X_1} \in A\} (A \subset {{\text{R}}^d}).$$


Empirical Process Discrete Apply Mathematic Basic Inequality Computational Learning Theory Asymptotic Minimax 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Luc Devroye
    • 1
  • Gábor Lugosi
    • 2
  1. 1.Computer Science DepartmentMcGill UniversityMontrealCanada
  2. 2.Facultat de Ciencies EconomiquesUniversitat Pompeu FabraBarcelonaSpain

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