Advertisement

Uniformity in the Underlying Distribution

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

Abstract

The previous chapters present empirical laws of large numbers and central limit theorems for observations from a fixed underlying distribution P. Many of the sufficient conditions given there are actually satisfied by very large classes of underlying measures; typically, the only limitation is finiteness of some appropriate moment of the envelope function. For instance, classes satisfying the uniform entropy condition are, up to measurability, Glivenko-Cantelli or Donsker for all P with P*F < ∞ or P*F 2 < ∞, respectively. In particular, many bounded classes of functions are universally Donsker: Donsker for every probability measure on the sample space.

Keywords

Central Limit Theorem Empirical Process Envelope Function Brownian Bridge Uniform Version 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations