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Processus empiriques, estimation non paramétrique et données censurées.

Abstract : The empirical process theory is a main topic is statistics, since it is involved in most of the general limit results dealing with random samples. In particular, uniform laws of the logarithm enabled to systematically handle the sup-norm convergence of kernel estimates. In this work, we first established uniform functional laws of the logarithm for the increments of the normed sample quantile process, enabling the derivation of new properties for k-nearest neighbors estimates. Similar results are obtained for the increments of the Kaplan-Meier empirical process, leading to uniform laws of the logarithm for both density and hazard rate estimates in presence of right-censoring. Turning our attention to the multivariate regression function, uniform-in-bandwidth laws of the logarithm are obtained for kernel estimates, especially in the censored case. Finally, we proposed an estimate of the censored regression function under the additive model assumption, enabling to get round the well-known curse of dimensionality. This estimate is essentially based on the marginal integration method.
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https://tel.archives-ouvertes.fr/tel-00119260
Contributor : Vivian Viallon <>
Submitted on : Friday, December 8, 2006 - 1:36:59 PM
Last modification on : Monday, December 14, 2020 - 9:52:35 AM
Long-term archiving on: : Thursday, September 20, 2012 - 3:41:08 PM

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  • HAL Id : tel-00119260, version 1

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Vivian Viallon. Processus empiriques, estimation non paramétrique et données censurées.. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2006. Français. ⟨tel-00119260⟩

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