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On hypothesis testing for Poisson processes: Regular case

Author

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

Abstract

We consider the problem of hypothesis testing in the situation when the firsthypothesis 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.

Suggested Citation

  • S. Dachian & Yu. A. Kutoyants & L. Yang, 2016. "On hypothesis testing for Poisson processes: Regular case," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(23), pages 6816-6832, December.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:23:p:6816-6832
    DOI: 10.1080/03610926.2014.968733
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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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