On Hypothesis 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 the thresholds and the power functions of the Score Function test, of the General Likelihood Ratio test, of the Wald test and of two Bayes tests in the situation when the intensity function of the observed 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: composite alternatives; asymptotic theory; regular situation; hypothesis testing; inhomogeneous Poisson processes

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

Serguei Dachian, Yury Kutoyants, Lin Yang. On Hypothesis Testing for Poisson Processes. Regular Case. Communications in Statistics - Theory and Methods, 2016, 45 (23), pp.6816-6832. ⟨hal-00967712v2⟩