Nonparametric tests for Cox processes

Benoît Cadre (1) , Gaspar Massiot (2) , Lionel Truquet (2, 1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz]

In a functional setting, we elaborate and study 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 count data. The limiting distributions of our statistics are derived using a functional central limit theorem for c`adì ag martingales. Our procedures are easily implementable and do not require any knowledge on the covariate. We address a theoretical comparison of the asymptotic power of our tests under some local alternatives. A numerical study reveals the good performances of the method. We also present two applications of our tests to real data sets.

Mots clés: Functional Statistic; Cox Process; Test Statistic; Local alternative; Nonparametric statistics

Domaines: Statistiques [math.ST]

Benoît Cadre, Gaspar Massiot, Lionel Truquet. Nonparametric tests for Cox processes. Journal of Statistical Planning and Inference, 2017, 184, pp.48-61. ⟨10.1016/j.jspi.2016.12.001⟩. ⟨hal-01430572⟩