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Some new almost sure results on the functional increments of the uniform empirical process

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  • Varron, Davit

Abstract

Given an observation of the uniform empirical process [alpha]n, its functional increments [alpha]n(u+an[dot operator])-[alpha]n(u) can be viewed as a single random process, when u is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate versions of these processes as n-->[infinity] and an[downwards arrow]0. Under mild conditions on an, a convergence in distribution and functional limit laws are established. The proofs rely on a new extension of the usual Poissonisation tools for the local empirical process.

Suggested Citation

  • Varron, Davit, 2011. "Some new almost sure results on the functional increments of the uniform empirical process," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 337-356, February.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:2:p:337-356
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    References listed on IDEAS

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    1. Berthet, Philippe, 2005. "Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 493-537, March.
    2. Einmahl, J. H.J., 1992. "The almost sure behavior of the weighted empirical process and the LIL for the weighted tail empirical process," Other publications TiSEM 5520438c-0aea-424b-b2c4-2, Tilburg University, School of Economics and Management.
    3. Deheuvels, Paul, 1992. "Functional laws of the iterated logarithm for large increments of empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 133-163, November.
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