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Two-step estimation procedures for inhomogeneous shot-noise Cox processes

Author

Listed:
  • Michaela Prokešová

    (Charles University in Prague)

  • Jiří Dvořák

    (Charles University in Prague)

  • Eva B. Vedel Jensen

    (Aarhus University)

Abstract

In the present paper, we discuss and compare several two-step estimation procedures for inhomogeneous shot-noise Cox processes. The intensity function is parametrized by the inhomogeneity parameters while the pair-correlation function is parametrized by the interaction parameters. The suggested procedures are based on a combination of Poisson likelihood estimation of the inhomogeneity parameters in the first step and an adaptation of a method from the homogeneous case for estimation of the interaction parameters in the second step. The adapted methods, based on minimum contrast estimation, composite likelihood and Palm likelihood, are compared both theoretically and by means of a simulation study. The general conclusion from the simulation study is that the three estimation methods have similar performance. Two-step estimation with Palm likelihood has not been considered before and is motivated by the superior performance of the Palm likelihood in the stationary case for estimation of certain parameters of interest. Asymptotic normality of the two-step estimator with Palm likelihood is proved.

Suggested Citation

  • Michaela Prokešová & Jiří Dvořák & Eva B. Vedel Jensen, 2017. "Two-step estimation procedures for inhomogeneous shot-noise Cox processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 513-542, June.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:3:d:10.1007_s10463-016-0556-y
    DOI: 10.1007/s10463-016-0556-y
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    References listed on IDEAS

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    1. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    2. Rasmus Waagepetersen & Yongtao Guan, 2009. "Two‐step estimation for inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 685-702, June.
    3. Michaela Prokešová & Eva Jensen, 2013. "Asymptotic Palm likelihood theory for stationary point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 387-412, April.
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    7. Yongtao Guan & Michael Sherman, 2007. "On least squares fitting for stationary spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 31-49, February.
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