Semi-Stable Non-Gaussian Laws Arising in Sampling of Finite Point Processes

• Activity Number: 685
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ritwik Chaudhuri*+ and Vladas Pipiras
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: finite point process ; sampling ; size distribution ; inversion ; semi-stable distribution

Abstract

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 process, that is, process obtained by sampling the points of i.i.d. realizations of the original point process. A standard non-parametric estimator of the size distribution has already been suggested in the literature, and has been shown to be asymptotically normal under suitable but strict assumptions. When these assumptions are not satisfied, it is shown here that the estimator can be attracted to semi-stable laws. 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.