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.
Classification : Primary 60G70, Secondary 62M30, 62G05
Mots clés : functional estimate, central limit theorem, moderate deviation principles, extreme values, shape estimation
@article{PS_2008__12__273_0,
author = {Menneteau, Ludovic},
title = {Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries},
journal = {ESAIM: Probability and Statistics},
pages = {273--307},
publisher = {EDP-Sciences},
volume = {12},
year = {2008},
doi = {10.1051/ps:2007039},
mrnumber = {2404032},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2007039/}
}
TY - JOUR AU - Menneteau, Ludovic TI - Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries JO - ESAIM: Probability and Statistics PY - 2008 DA - 2008/// SP - 273 EP - 307 VL - 12 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2007039/ UR - https://www.ams.org/mathscinet-getitem?mr=2404032 UR - https://doi.org/10.1051/ps:2007039 DO - 10.1051/ps:2007039 LA - en ID - PS_2008__12__273_0 ER -
Menneteau, Ludovic. Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 273-307. doi : 10.1051/ps:2007039. http://www.numdam.org/articles/10.1051/ps:2007039/
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