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Functional laws of the iterated logarithm for small increments of empirical processes

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  • P. Deheuvels

Abstract

Let F, denote the uniform empirical distribution based on the first n ≥ 1 observations from an i.i.d. sequence of uniform (0, 1) random variables. We describe the almost sure limiting behavior of the sets of increment functions {Fn(t + hn.) ‐ Fn(t): 0 ≤t ≤ 1 ‐ hn}, when {hn: n ≥ 1) is a nonincreasing sequence of constants such that nhn/log n ← 0.

Suggested Citation

  • P. Deheuvels, 1996. "Functional laws of the iterated logarithm for small increments of empirical processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 50(2), pages 261-280, July.
    • Handle: RePEc:bla:stanee:v:50:y:1996:i:2:p:261-280
    DOI: 10.1111/j.1467-9574.1996.tb01493.x
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    Cited by:

    1. Dindar, Zacharie, 2003. "Some more results on increments of the partially observed empirical process," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 25-37, August.
    2. Djamal Louani & Alain Lucas, 2003. "Fractal Dimensions for Some Increments of the Uniform Empirical Process," Journal of Theoretical Probability, Springer, vol. 16(1), pages 59-86, January.
    3. Einmahl, J.H.J. & Deheuvels, P., 2000. "Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications," Other publications TiSEM ac9bbdc0-62f8-4b48-9a84-1, Tilburg University, School of Economics and Management.

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