Asymptotic gaussianity of some estimators for reduced factorial moment measures and product densities of stationary poisson cluster processes

Publisher Website
Google Scholar
Abstract
The main purpose of this paper is to present cer~trai limit tileoreins including functional limit theorems for empirical factorial moment measures and kernel-type product density estimators when the underlying point process is a regular infinitely divisible one.The requied moment conditions are minimal, they are necessary to ensure finite variances of the estimators under consideration. In the special case of a stationary poisson process the obtained results are used to construct a goodness-of-fit test for the function λK(t), 0≤t≤T, denoting the mean number of points within a sphere with radius t around a typical point of the process.

This publication has 13 references indexed in Scilit: