Some new almost sure results on the functional increments of the uniform empirical process |
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Authors: | Davit Varron |
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Affiliation: | Université de Franche-Comté, CNRS, Laboratoire de Mathématiques Pures et Appliquées, UMR CNRS 6623, 16, route de Gray, 25030 Besançon Cedex, France |
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Abstract: | Given an observation of the uniform empirical process αn, its functional increments αn(u+an⋅)−αn(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→∞ and an↓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. |
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Keywords: | Empirical processes Functional limit theorems |
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