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.
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Philipp, W., Pinzur, L. Almost sure approximation theorems for the multivariate empirical process. Z. Wahrscheinlichkeitstheorie verw Gebiete 54, 1–13 (1980). https://doi.org/10.1007/BF00535346
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DOI: https://doi.org/10.1007/BF00535346