On Hypotheses Testing for Poisson Processes. Singular Cases

Serguei Dachian (1) , Yury Kutoyants (2) , Lin Yang (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LMM - Laboratoire Manceau de Mathématiques

We consider the problem of hypotheses testing in the situation where the first hypothesis is simple and the second one is one-sided local composite. We describe the choice of thresholds and the power functions of different tests when the intensity function of the inhomogeneous Poisson process has two different types of singularity: cusp and discontinuity. The asymptotic results are illustrated by the numerical simulations.

Mots clés: hypotheses testing; Poisson processes; asymptotic theory; composite alternatives; singular situations

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Serguei Dachian, Yury Kutoyants, Lin Yang. On Hypotheses Testing for Poisson Processes. Singular Cases. 2014. ⟨hal-00967716v1⟩