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Lois limites uniformes et estimation non-paramétrique de la régression

Abstract : We use general empirical process theory methods to determine exact rates of strong uniform consistency of kernel-type estimators of the regression function including local polynomial estimators. Our theorems take form of uniform limit laws of the logarithm in the same spirit of results by Deheuvels and Mason (2004). The core of the proof relies on a remarkable exponential inequality concerning the probability of deviation from the mean for suprema of empirical processes indexed by classes of functions. We extend also this method of proof to the semiparametric setup, i.e. when the conditional distribution is parametred, and we prove a uniform limit law for the local maximum likelihood estimator.
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https://tel.archives-ouvertes.fr/tel-00011943
Contributor : David Blondin <>
Submitted on : Tuesday, March 14, 2006 - 4:18:53 PM
Last modification on : Wednesday, December 9, 2020 - 3:12:29 PM
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  • HAL Id : tel-00011943, version 1

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David Blondin. Lois limites uniformes et estimation non-paramétrique de la régression. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2004. Français. ⟨tel-00011943⟩

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