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A weighted estimating equation approach for inhomogeneous spatial point processes

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  • Yongtao Guan
  • Ye Shen

Abstract

We introduce a new estimation method for parametric intensity function models of inhomogeneous spatial point processes based on weighted estimating equations. The weights can incorporate information on both inhomogeneity and dependence of the process. Simulations show that significant efficiency gains can be achieved for non-Poisson processes, compared to the Poisson maximum likelihood estimator. An application to tropical forest data illustrates the use of the proposed method. Copyright 2010, Oxford University Press.

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  • Yongtao Guan & Ye Shen, 2010. "A weighted estimating equation approach for inhomogeneous spatial point processes," Biometrika, Biometrika Trust, vol. 97(4), pages 867-880.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:4:p:867-880
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    File URL: http://hdl.handle.net/10.1093/biomet/asq043
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    Cited by:

    1. Zheng, Xueying & Xue, Lan & Qu, Annie, 2018. "Time-varying correlation structure estimation and local-feature detection for spatio-temporal data," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 221-239.
    2. Daniel, Jeffrey & Horrocks, Julie & Umphrey, Gary J., 2018. "Penalized composite likelihoods for inhomogeneous Gibbs point process models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 104-116.
    3. Chong Deng & Yongtao Guan & Rasmus P. Waagepetersen & Jingfei Zhang, 2017. "Second‐order quasi‐likelihood for spatial point processes," Biometrics, The International Biometric Society, vol. 73(4), pages 1311-1320, December.
    4. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2024. "Goodness-of-fit test for point processes first-order intensity," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    5. Federico Ferraccioli & Eleonora Arnone & Livio Finos & James O. Ramsay & Laura M. Sangalli, 2021. "Nonparametric density estimation over complicated domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 346-368, April.
    6. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.
    7. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2020. "Bootstrapping kernel intensity estimation for inhomogeneous point processes with spatial covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    8. Zhang, Tonglin & Mateu, Jorge, 2019. "Substationarity for spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 22-36.

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