Document 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 MenneteauPlace 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