Statistics/Probability Theory
M-processes and applications
Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 265-270.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.11.029
Chebana, Fateh 1

1 Université du Québec, INRS-ETE, 490, de la Couronne, G1K 9A9 Québec QC, Canada
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Chebana, Fateh. M-processes and applications. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 265-270. doi : 10.1016/j.crma.2006.11.029. http://www.numdam.org/articles/10.1016/j.crma.2006.11.029/

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