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


This part is concerned with convergence of a particular type of random map: the empirical process. The empirical measure n of a sample of random elements X 1i,...,X n on a measurable space (X, A) is the discrete random measure given by ℙ n (C) = n −1#(1 ≤ in: X i C). Alternatively (if points are measurable), it can be described as the random measure that puts mass 1/n at each observation. We shall frequently write the empirical measure as the linear combination \({{\rm P}_n} = {n^{ - 1}}\sum _{i = 1}^n{\delta _{{X_i}}}\) of the dirac measures at the observations.


Central Limit Theorem Outer Probability Empirical Process Empirical Distribution Function Brownian Bridge 
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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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