Tail Bounds

  • Aad W. van der Vaart
  • Jon A. Wellner
Part of the Springer Series in Statistics book series (SSS)

Abstract

In this chapter we derive moment and tail bounds for the supremum \( \left\| {{G_n}} \right\|F \) of the empirical process. Throughout this chapter, \( {G_{n = \sqrt n }}({P_n} - P) \) denotes the empirical process of an i.i.d. sample X 1,..., X n ,, from a probability measure P, defined as the coordinate projections of a product probability space (X , A , P ).

Keywords

Central Limit Theorem Universal Constant Empirical Process Tail Probability Envelope Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Aad W. van der Vaart
    • 1
  • Jon A. Wellner
    • 2
  1. 1.Department of Mathematics and Computer ScienceFree UniversityAmsterdamThe Netherlands
  2. 2.StatisticsUniversity of WashingtonSeattleUSA

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