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

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

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

Serguei Dachian, Yury Kutoyants, Lin Yang. On Hypothesis Testing for Poisson Processes. Singular Cases. Communications in Statistics - Theory and Methods, 2016, 45 (23), pp.6833-6859. ⟨hal-00967716v2⟩