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

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  • Sergio Alvarez-Andrade
  • Salim Bouzebda
  • Aimé Lachal

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.

Suggested Citation

  • Sergio Alvarez-Andrade & Salim Bouzebda & Aimé Lachal, 2017. "Some asymptotic results for the integrated empirical process with applications to statistical tests," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(7), pages 3365-3392, April.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:7:p:3365-3392
    DOI: 10.1080/03610926.2015.1060346
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