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

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

Received: 11 March 2005
Revised: 26 June 2006
Revised: 26 March 2007

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.