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Asymptotic Palm likelihood theory for stationary point processes

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  • Michaela Prokešová
  • Eva Jensen

Abstract

In the present paper, we propose a Palm likelihood approach as a general estimating principle for stationary point processes in $$\mathbf{R}^d$$ for which the density of the second-order factorial moment measure is available in closed form or in an integral representation. Examples of such point processes include the Neyman–Scott processes and the log Gaussian Cox processes. The computations involved in determining the Palm likelihood estimator are simple. Conditions are provided under which the Palm likelihood estimator is strongly consistent and asymptotically normally distributed. Copyright The Institute of Statistical Mathematics, Tokyo 2013

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  • 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.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:2:p:387-412
    DOI: 10.1007/s10463-012-0376-7
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    Cited by:

    1. Frédéric Lavancier & Arnaud Poinas & Rasmus Waagepetersen, 2021. "Adaptive estimating function inference for nonstationary determinantal point processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 87-107, March.
    2. Jean-François Coeurjolly, 2017. "Median-based estimation of the intensity of a spatial point process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 303-331, April.
    3. James S. Martin & David J. Murrell & Sofia C. Olhede, 2023. "Multivariate geometric anisotropic Cox processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1420-1465, September.
    4. Ben C. Stevenson & David L. Borchers & Rachel M. Fewster, 2019. "Cluster capture‐recapture to account for identification uncertainty on aerial surveys of animal populations," Biometrics, The International Biometric Society, vol. 75(1), pages 326-336, March.
    5. 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.
    6. Ushio Tanaka & Yosihiko Ogata, 2014. "Identification and estimation of superposed Neyman–Scott spatial cluster processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 687-702, August.
    7. Schatz, Michael & Wheatley, Spencer & Sornette, Didier, 2022. "The ARMA Point Process and its Estimation," Econometrics and Statistics, Elsevier, vol. 24(C), pages 164-182.
    8. Poinas, Arnaud, 2019. "A bound of the β-mixing coefficient for point processes in terms of their intensity functions," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 88-93.

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