Strong approximations for the p-fold integrated empirical process with applications to statistical tests

Sergio Alvarez-Andrade (), Salim Bouzebda () and Aimé Lachal ()
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Sergio Alvarez-Andrade: Université de Technologie de Compiègne
Salim Bouzebda: Université de Technologie de Compiègne
Aimé Lachal: Université de Lyon

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 4, No 8, 826-849

Abstract: Abstract The main purpose of this paper is to investigate the strong approximation of the p-fold integrated empirical process, p being a fixed positive integer. 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. (Z Wahrscheinlichkeitstheorie und Verw Gebiete 32:111–131, 1975)’s results. Applications include the two-sample testing procedures together with the change-point problems. Finally, simulation results are provided to illustrate the finite sample performance of the proposed statistical tests based on the integrated empirical processes.

Keywords: Integrated empirical process; Brownian bridge; Kiefer process; Rates of convergence; Two-sample problem; Hypothesis testing; Goodness-of-fit; Change-point; Primary 62G30; 62G20; 60F17; Secondary 62F03; 62F12; 60F15 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11749-017-0572-0

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