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arXiv · 1505.07345

Some asymptotic results for the integrated empirical process with applications to statistical tests

Sergio Alvarez-Andrade·Salim Bouzebda·Aimé Lachal
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Abstract

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Koml\'os, Major and Tusn\'ady's results. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of the integrated empirical process when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial sum process representation of the integrated empirical process. Reference: Koml\'os, J., Major, P. and Tusn\'ady, G. (1975). An approximation of partial sums of independent RV's and the sample DF. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 32, 111-131.

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Sergio Alvarez-Andrade, Salim Bouzebda, Aimé Lachal. 2015-05-27. Some asymptotic results for the integrated empirical process with applications to statistical tests. https://doi.org/10.1080/03610926.2015.1060346

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