On the Rate of Clustering to the Strassen Set for Increments of the Uniform Empirical Process

Philippe Berthet ()

Journal of Theoretical Probability, 1997, vol. 10, issue 3, 557-579

Abstract: Abstract We obtain outer rates of clustering in the functional laws of the iterated logarithm of Deheuvels and Mason(11) and Deheuvels,(7) which describe local oscillations of empirical processes. Considering increment sizes a n ↓ 0 such that na n ↑ ∞ and na n(log n)−7/3 → ∞ we show that the sets of properly rescaled increment functions cluster with probability one to the ε n-enlarged Strassen ball in B(0, 1) endowed with the uniform topology, where ε n ↓ 0 may be chosen so small as ε(log (1/a n) + log log n)−2/3 for any sufficiently large ε. This speed of coverage is reduced for smaller a n.

Keywords: Empirical processes; functional limit laws; laws of the iterated logarithm; rates of clustering (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022632825288

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