Tail Bounds

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


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 ).


Central Limit Theorem Universal Constant Empirical Process Tail Probability Envelope Function 
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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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