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Journal of Theoretical Probability

, Volume 7, Issue 1, pp 73–118 | Cite as

Komlos-Major-Tusnady approximation for the general empirical process and Haar expansions of classes of functions

  • Vladimir I. Koltchinskii
Article

Abstract

Rates of convergence of the Komlos-Major-Tusnady type in the invariance principle for empirical processes indexed by functions are obtained. The conditions are given in terms of the empirical entropy and the accuracy of the Haar type approximation for the corresponding classes of functions. The recent results of Massart(25) as well as some new results for empirical characteristic functions are obtained as a corollary.

Key Words

Empirical processes KMT-approximation Brownian bridge empirical entropy Haar basis 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Vladimir I. Koltchinskii
    • 1
    • 2
  1. 1.Department of Probability and StatisticsKiev State UniversityKievUkraine
  2. 2.Department of MathematicsUniversity of ConnecticutStorrs

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