2016/03/22 by Benoı̂t Cadre, Cadre, Benoît, Gaspar Massiot +3
Computer Science · Mathematics · #60G44 #62C12 #62M07 #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1603.06786
openalex publication_date 2016/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.