Open Access
May 2016 Non-Gaussian semi-stable laws arising in sampling of finite point processes
Ritwik Chaudhuri, Vladas Pipiras
Bernoulli 22(2): 1055-1092 (May 2016). DOI: 10.3150/14-BEJ686


A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer this size distribution from the observed sizes of sampled point processes, that is, processes obtained by sampling independently the points of i.i.d. realizations of the original point process. A standard nonparametric estimator of the size distribution has already been suggested in the literature, and has been shown to be asymptotically normal under suitable but restrictive assumptions. When these assumptions are not satisfied, it is shown here that the estimator can be attracted to a semi-stable law. The assumptions are discussed in the case of several concrete examples. A major theoretical contribution of this work are new and quite general sufficient conditions for a sequence of i.i.d. random variables to be attracted to a semi-stable law.


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Ritwik Chaudhuri. Vladas Pipiras. "Non-Gaussian semi-stable laws arising in sampling of finite point processes." Bernoulli 22 (2) 1055 - 1092, May 2016.


Received: 1 December 2013; Revised: 1 October 2014; Published: May 2016
First available in Project Euclid: 9 November 2015

zbMATH: 06562305
MathSciNet: MR3449808
Digital Object Identifier: 10.3150/14-BEJ686

Keywords: domain of attraction , finite point process , sampling , semi-stable law

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 2 • May 2016
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