On the Approximation of Quantile Processes by Kiefer Processes

Paul Deheuvels

Journal of Theoretical Probability, 1998, vol. 11, issue 4, 997-1018

Abstract: Abstract We prove that the best possible almost sure rate of uniform approximation of a uniform quantile process by a normed Kiefer process is O(n −1/4(log n)1/2× (log log n)1/4).

Keywords: Empirical processes; quantile processes; order statistics; law of iterated logarithm; almost sure convergence; strong laws; strong invariance principles; strong approximation; Kiefer processes; Wiener processes (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022668932637

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