ESAIM: Probability and Statistics

Table of Contents - 2008 - Volume 12  

Research Article

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

Menneteau, Ludovic

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

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.

(Received March 11 2005)

(Revised June 26 2006)

(Revised March 26 2007)

(Online publication May 8 2008)

Key Words:

  • Functional estimate;
  • central limit theorem;
  • moderate deviation principles;
  • extreme values;
  • shape estimation

Mathematics Subject Classification:

  • Primary 60G70; Secondary 62M30;
  • 62G05
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