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

Sergio Alvarez-Andrade, Salim Bouzebda and Aimé Lachal

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 7, 3365-3392

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 Komlós et al. (1975)'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.

Date: 2017
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DOI: 10.1080/03610926.2015.1060346

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