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On APF test for Poisson process with shift and scale parameters

Author

Listed:
  • Dabye, A.S.
  • Kutoyants, Yu.A.
  • Tanguep, E.D.

Abstract

We propose the goodness of fit test for inhomogeneous Poisson processes with unknown scale and shift parameters. A test statistic of Cramér–von Mises type is proposed and its asymptotic behavior is studied. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameters.

Suggested Citation

  • Dabye, A.S. & Kutoyants, Yu.A. & Tanguep, E.D., 2019. "On APF test for Poisson process with shift and scale parameters," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 28-36.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:28-36
    DOI: 10.1016/j.spl.2018.08.001
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    References listed on IDEAS

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    1. Yury Kutoyants, 2014. "On asymptotic distribution of parameter free tests for ergodic diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 139-161, July.
    2. Lionel Weiss, 1975. "Testing fit with nuisance location and scale parameters," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(1), pages 55-63, March.
    3. A. Dabye, 2013. "On the Cramér–von Mises test with parametric hypothesis for poisson processes," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 1-13, April.
    4. M. Kleptsyna & Yu. Kutoyants, 2014. "On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 295-319, October.
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