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

Central limit theorems for smoothed extreme value estimates of Poisson point processes bound\-aries
Authors: Girard, Stéphane; Menneteau, Ludovic;

Central limit theorems for smoothed extreme value estimates of Poisson 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.

Country
France
Keywords

[STAT.ME] Statistics [stat]/Methodology [stat.ME], Inference from spatial processes, functional estimate, Mathematics - Statistics Theory, Poisson process, Statistics Theory (math.ST), 510, Extreme value theory; extremal stochastic processes, boundary estimation, Asymptotic properties of nonparametric inference, FOS: Mathematics, Nonparametric estimation, [STAT.ME]Statistics [stat]/Methodology [stat.ME]

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
11
Average
Top 10%
Top 10%
Green
bronze
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