A nonparametric test for Cox processes
Abstract
In a functional setting, we propose two test statistics to highlight the Poisson nature of a Cox process when n copies of the process are available. Our approach involves a comparison of the empirical mean and the empirical variance of the functional data and can be seen as an extended version of a classical overdispersion test for counting data. The limiting distributions of our statistics are derived using a functional central limit theorem for c`adl`ag martingales. We also study the asymptotic power of our tests under some local alternatives. Our procedure is easily implementable and does not require any knowledge of covariates. A numerical study reveals the good performances of the method. We also present two applications of our tests to real data sets.
Cite
@article{arxiv.1603.06786,
title = {A nonparametric test for Cox processes},
author = {Benoît Cadre and Gaspar Massiot and Lionel Truquet},
journal= {arXiv preprint arXiv:1603.06786},
year = {2016}
}