Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 273-307.

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.

DOI : 10.1051/ps:2007039
Classification : Primary 60G70, Secondary 62M30, 62G05
Mots clés : functional estimate, central limit theorem, moderate deviation principles, extreme values, shape estimation
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     author = {Menneteau, Ludovic},
     title = {Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2007039/}
}
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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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