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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 limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided.

Keywords

Functional estimatecentral limit theoremmoderate deviation principlesextreme valuesshape estimation
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 273 - 307
Copyright
© EDP Sciences, SMAI, 2008

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