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Journal Articles Journal of Statistical Planning and Inference Year : 2005

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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Dates and versions

hal-00383141 , version 1 (12-05-2009)
hal-00383141 , version 2 (13-03-2014)

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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, 2005, 135 (2), pp.433-460. ⟨10.1016/j.jspi.2004.04.020⟩. ⟨hal-00383141v2⟩
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