Abstract
Mason and van Zwet gave an approximation of the uniform empirical process by a Brownian bridge. Their result is a refinement of a result of Komlos, Major and Tusnady in the case when the process is considered in a small interval. In this note we show that in such cases a much better Poissonian approximation is possible which seems to be better applicable in certain cases. We also prove a multidimensional version of this result, where a sequence of uniform empirical processes is simultaneously approximated by partial sums of independent Poisson processes.
Citation
Peter Major. "A Note on the Approximation of the Uniform Empirical Process." Ann. Probab. 18 (1) 129 - 139, January, 1990. https://doi.org/10.1214/aop/1176990941
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