Comptes Rendus
no. 12
Probability Theory
A functional Hungarian construction for the sequential empirical process
[Une construction hongroise fonctionnelle pour le processus empirique séquentiel]

Présenté par : Michel Talagrand

Michael Jähnisch1 ; Michael Nussbaum2
1 SAP AG, Neurottstrasse 16, 69190 Walldorf, Germany
2 Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
Comptes Rendus. Mathématique, Volume 341 (2005) no. 12, pp. 761-763.

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 H, mais le supremum est pris en dehors de la probabilité. Comparé au couplage en norme sup, ceci permet des classes de fonctions H plus larges. Le résultat peut être utilisé pour démontrer l'équivalence asymptotique de certaines expériences statistiques non-paramétriques.

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 H, but the supremum over f∈H is taken outside the probability. Compared to the coupling in sup-norm, this allows for larger functional classes H. The result is useful for proving asymptotic equivalence of certain nonparametric statistical experiments.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2005.10.022
Michael Jähnisch 1 ; Michael Nussbaum 2

1 SAP AG, Neurottstrasse 16, 69190 Walldorf, Germany
2 Department of Mathematics, Cornell University, Ithaca, NY 14853, USA 
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Michael Jähnisch; Michael Nussbaum. A functional Hungarian construction for the sequential empirical process. Comptes Rendus. Mathématique, Volume 341 (2005) no. 12, pp. 761-763. doi : 10.1016/j.crma.2005.10.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.022/

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