Comptes Rendus
no. 12
Probability Theory
A functional Hungarian construction for the sequential empirical process

Presented by: 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.

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.

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.

Received:
Accepted:
Published online:
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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