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On hypothesis testing for Poisson processes. Singular cases |
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| Authors: | S Dachian Yu A Kutoyants |
| Institution: | 1. Paul Painlevé Laboratory, University of Lille 1, Lille, France;2. “RTD &3. AS” Department, National Research University “MPEI”, Moscow, Russia;4. “RTD &5. Mathematics Department, University of Maine, Le Mans, France |
| Abstract: | ABSTRACTWe consider the problem of hypothesis testing in the situation where the first hypothesis is simple and the second one is local one-sided composite. Wedescribe 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. |
| Keywords: | Asymptotic theory Composite alternatives Hypothesis testing Inhomogeneous Poisson processes Singular situations |