On Hypotheses Testing for Poisson Processes. Regular Case

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 when the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of thresholds and the power functions of Score-function test, General Likelihood Ratio test, Bayesian tests and Wald test in the situation when the intensity function of inhomogeneous Poisson process is smooth with respect to the parameter. It is shown that almost all these tests are asymptotically uniformly most powerful. The results of numerical simulations are presented.

Mots clés: hypotheses testing; inhomogeneous Poisson processes; asymptotic theory; composite alternatives; regular situation

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

Serguei Dachian, Yury Kutoyants, Lin Yang. On Hypotheses Testing for Poisson Processes. Regular Case. 2014. ⟨hal-00967712v1⟩