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Issue ESAIM: PS
Volume 12
Page(s) 273 - 307
DOI 10.1051/ps:2007039
Published online 08 May 2008

ESAIM: PS, April 2008, Vol. 12, p. 273-307
DOI: 10.1051/ps:2007039

Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries

Ludovic Menneteau

Place Eugène Bataillon, 34095 Montpellier Cedex 5, France; mennet@math.univ-montp2.fr


Received March 11, 2005. Revised June 26, 2006 and March 26, 2007. Published online 8 May 2008

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.


Mathematics Subject Classification. Primary 60G70; Secondary 62M30, 62G05

Key words: Functional estimate, central limit theorem, moderate deviation principles, extreme values, shape estimation


© EDP Sciences, SMAI 2008


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