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Identification and estimation of superposed Neyman–Scott spatial cluster processes

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  • Ushio Tanaka
  • Yosihiko Ogata

Abstract

This paper proposes an estimation method for superposed spatial point patterns of Neyman–Scott cluster processes of different distance scales and cluster sizes. Unlike the ordinary single Neyman–Scott model, the superposed process of Neyman–Scott models is not identified solely by the second-order moment property of the process. To solve the identification problem, we use the nearest neighbor distance property in addition to the second-order moment property. In the present procedure, we combine an inhomogeneous Poisson likelihood based on the Palm intensity with another likelihood function based on the nearest neighbor property. The derivative of the nearest neighbor distance function is regarded as the intensity function of the rotation invariant inhomogeneous Poisson point process. The present estimation procedure is applied to two sets of ecological location data. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:4:p:687-702
    DOI: 10.1007/s10463-013-0431-z
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    1. 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.
    2. Guan, Yongtao, 2006. "A Composite Likelihood Approach in Fitting Spatial Point Process Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1502-1512, December.
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    4. Tomáš Mrkvička & Ilya Molchanov, 2005. "Optimisation of linear unbiased intensity estimators for point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 71-81, March.
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