Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries
Place Eugène Bataillon, 34095 Montpellier Cedex 5, France; firstname.lastname@example.org
Revised: 26 June 2006
Revised: 26 March 2007
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