Multiplier Central Limit Theorems

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


With the notation Z i x i P, the empirical central limit theorem can be written
$$ \frac{1}{{\sqrt n }}\sum\limits_{i = 1}^n {{Z_i}} \rightsquigarrow G $$
in e∞(F), where G is a (tight) Brownian bridge. Given i.i.d. real-valued random variables ξi,..., ξ n , which are independent of Z1,..., Z n , the multiplier central limit theorem asserts that
$$ \frac{1}{{\sqrt n }}\sum\limits_{i = 1}^n {{\xi _i}{Z_i}} \rightsquigarrow G $$


Central Limit Theorem Empirical Process Brownian Bridge Symmetric Variable Conditional Convergence 
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.


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