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Almost sure approximation theorems for the multivariate empirical process

  • Walter Philipp
  • Laurence Pinzur
Article

Summary

Let R(s,t) be the empirical process of a sequence of independent random vectors with common but arbitrary distribution function. In this paper we give an almost sure approximation of R(s,t) by a Kiefer process. The result continues to hold for stationary sequences of random vectors with continuous distribution function and satisfying a strong mixing condition.

Keywords

Distribution Function Stochastic Process Probability Theory Random Vector Mathematical Biology 
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-Verlag 1980

Authors and Affiliations

  • Walter Philipp
    • 1
  • Laurence Pinzur
    • 2
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Hewitt AssociatesStamfordUSA

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