Permanence of the Donsker Property

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


In this chapter we consider a number of operations that preserve the Donsker property and allow the formation of many new Donsker classes from given examples. For instance, unions, convex hulls, and certain closures of Donsker classes are Donsker. The main result of this chapter concerns Lipschitz transformations of Donsker classes and is discussed in Section 2.10.2. Section 2.10.3 covers the preservation of the uniform-entropy condition, and in Section 2.10.4 new Donsker classes are formed through union of sample spaces.


Convex Hull Outer Probability Empirical Process Entropy Condition 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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