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Multidimensional limit theorems for smoothed extreme value estimates of pointprocesses boundaries

Published online by Cambridge University Press:  08 May 2008

Ludovic Menneteau
Ludovic Menneteau*
Affiliation:
Place Eugène Bataillon, 34095 Montpellier Cedex 5, France; mennet@math.univ-montp2.fr
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Abstract

In this paper, we give sufficient conditions to establish central limittheorems and moderate deviation principle for a class of support estimates ofempirical and Poisson point processes. The considered estimates are obtained bysmoothing some bias corrected extreme values of the point process. We show howthe smoothing permits to obtain Gaussian asymptotic limits and thereforepointwise confidence intervals. Some unidimensional and multidimensionalexamples are provided.

Keywords

Functional estimatecentral limit theoremmoderate deviation principlesextreme valuesshape estimation

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 273 - 307
Copyright
© EDP Sciences, SMAI, 2008

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