Abstract
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. To cite this article: F. Chebana, C. R. Acad. Sci. Paris, Ser. I 344 (2007).
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