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Comptes Rendus Mathématique
Volume 341, n° 12
pages 761-763 (décembre 2005)
Doi : 10.1016/j.crma.2005.10.022
Received : 11 October 2005 ;  accepted : 18 October 2005
A functional Hungarian construction for the sequential empirical process
Une construction hongroise fonctionnelle pour le processus empirique séquentiel
 

Michael Jähnisch a , Michael Nussbaum b, 1
a SAP AG, Neurottstrasse 16, 69190 Walldorf, Germany 
b Department of Mathematics, Cornell University, Ithaca, NY 14853, USA 

Abstract

We establish a KMT coupling for the sequential empirical process and the Kiefer-Müller process. The processes are indexed by functions f from a Hölder class  , but the supremum over   is taken outside the probability. Compared to the coupling in sup-norm, this allows for larger functional classes  . The result is useful for proving asymptotic equivalence of certain nonparametric statistical experiments. To cite this article: M. Jähnisch, M. Nussbaum, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Résumé

Nous établissons un couplage KMT pour le processus empirique séquentiel et le processus de Kiefer-Müller. Les processus sont indexés par des fonctions f appartenant à une classe de Hölder  , mais le supremum est pris en dehors de la probabilité. Comparé au couplage en norme sup, ceci permet des classes de fonctions   plus larges. Le résultat peut être utilisé pour démontrer lʼéquivalence asymptotique de certaines expériences statistiques non-paramétriques. Pour citer cet article : M. Jähnisch, M. Nussbaum, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
1  Research supported by the National Science Foundation under grant DMS0306497.


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