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

• Sergio Alvarez-Andrade ^[1] ; Salim Bouzebda ^[1] ; Aimé Lachal ^[2]
  1. [1] University of Technology of Compiègne

     University of Technology of Compiègne

     Arrondissement de Compiègne, Francia

     
  2. [2] University of Lyon System

     University of Lyon System

     Arrondissement de Lyon, Francia

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 27, Nº. 4, 2018, págs. 826-849
• Idioma: inglés
• DOI: 10.1007/s11749-017-0572-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.