Almost sure approximation theorems for the multivariate empirical process

  • Walter Philipp
  • Laurence Pinzur


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.


Distribution Function Stochastic Process Probability Theory Random Vector Mathematical Biology 
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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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