<i>M</i>-processes and applications

Fateh Chebana

doi:10.1016/j.crma.2006.11.029

Statistics/Probability Theory

M-processes and applications

Presented by: Paul Deheuvels

Fateh Chebana ¹

¹ Université du Québec, INRS-ETE, 490, de la Couronne, G1K 9A9 Québec QC, Canada

Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 265-270.

Abstract
Résumé

We consider a class of M-estimators indexed by the criterion function ψ which belongs to a class of functions $F$ . Then, we obtain a process indexed by the class $F$ . The convergence in probability of these processes is studied uniformly on $F$ when the parameter to be estimated is the same for all functions ψ. We also establish their weak convergence towards a Gaussian process. We illustrate these results on a location estimation example.

Nous considérons une classe de M-estimateurs en faisant varier la fonction critère ψ dans une classe de fonctions $F$ . Nous obtenons ainsi un processus indexé par cette classe $F$ . Dans le cas où le paramètre à estimer est le même pour toutes les fonctions ψ, nous étudions la convergence en probabilité de ce processus uniformément sur la classe $F$ . Nous établissons également sa convergence faible vers un processus gaussien. Nous illustrons ces résultats sur un exemple d'estimation de paramètre de position.

Received: 2004-10-25
Accepted: 2006-11-21
Published online: 2007-01-26

DOI: 10.1016/j.crma.2006.11.029

Author's affiliations:

Fateh Chebana ¹

¹ Université du Québec, INRS-ETE, 490, de la Couronne, G1K 9A9 Québec QC, Canada

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     author = {Fateh Chebana},
     title = {\protect\emph{M}-processes and applications},
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     language = {en},
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Fateh Chebana. M-processes and applications. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 265-270. doi : 10.1016/j.crma.2006.11.029. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.029/

References
Cited by

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[5] S. van de Geer Empirical processes in M-estimation, 2003 http://cowles.econ.yale.edu/conferences/wkshp/lec/geer.pdf (Technical report, Cowles Workshop, Yales University)

[6] S.A. van de Geer Applications of Empirical Process Theory, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 2000

[7] A.W. van der Vaart Asymptotic Statistics, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 1998

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