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On hypothesis testing for Poisson processes. Singular cases

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  • S. Dachian
  • Yu. A. Kutoyants
  • L. Yang

Abstract

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. 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.

Suggested Citation

  • S. Dachian & Yu. A. Kutoyants & L. Yang, 2016. "On hypothesis testing for Poisson processes. Singular cases," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(23), pages 6833-6859, December.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:23:p:6833-6859
    DOI: 10.1080/03610926.2014.968734
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    Cited by:

    1. Arij Amiri & Sergueï Dachian, 2021. "On smooth change-point location estimation for Poisson Processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 499-524, October.

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