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.
@article{1176990941,
author = {Major, Peter},
title = {A Note on the Approximation of the Uniform Empirical Process},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 129-139},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990941}
}
Major, Peter. A Note on the Approximation of the Uniform Empirical Process. Ann. Probab., Tome 18 (1990) no. 4, pp. 129-139. http://gdmltest.u-ga.fr/item/1176990941/