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

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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https://hal.inria.fr/hal-00383141
Contributor : Stephane Girard <>
Submitted on : Thursday, March 13, 2014 - 10:08:58 AM
Last modification on : Friday, May 28, 2021 - 3:58:03 PM
Long-term archiving on: : Friday, June 13, 2014 - 11:00:48 AM

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Stéphane Girard, Ludovic Menneteau. Central limit theorems for smoothed extreme value estimates of point processes boundaries. Journal of Statistical Planning and Inference, Elsevier, 2005, 135 (2), pp.433-460. ⟨10.1016/j.jspi.2004.04.020⟩. ⟨hal-00383141v2⟩

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