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

Ludovic Menneteau

ESAIM: Probability and Statistics (2008)

  • Volume: 12, page 273-307
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Menneteau, Ludovic. "Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries." ESAIM: Probability and Statistics 12 (2008): 273-307. <http://eudml.org/doc/250410>.

@article{Menneteau2008,
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. },
author = {Menneteau, Ludovic},
journal = {ESAIM: Probability and Statistics},
keywords = {Functional estimate; central limit theorem; moderate deviation principles; extreme values; shape estimation; functional estimate},
language = {eng},
month = {5},
pages = {273-307},
publisher = {EDP Sciences},
title = {Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries},
url = {http://eudml.org/doc/250410},
volume = {12},
year = {2008},
}

TY - JOUR
AU - Menneteau, Ludovic
TI - Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries
JO - ESAIM: Probability and Statistics
DA - 2008/5//
PB - EDP Sciences
VL - 12
SP - 273
EP - 307
AB - 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.
LA - eng
KW - Functional estimate; central limit theorem; moderate deviation principles; extreme values; shape estimation; functional estimate
UR - http://eudml.org/doc/250410
ER -

References

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