Introduction

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

Abstract

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.

Keywords

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

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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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