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arXiv · 1103.5884

Central limit theorems for smoothed extreme value estimates of Poisson point processes boundaries

Stéphane Girard·Ludovic Menneteau
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Abstract

In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing leads Gaussian asymptotic distributions and therefore pointwise confidence intervals. Some new unidimensional and multidimensional examples are provided.

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Stéphane Girard, Ludovic Menneteau. 2011-03-30. Central limit theorems for smoothed extreme value estimates of Poisson point processes boundaries. https://arxiv.org/abs/1103.5884

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