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Variance estimation for statistics computed from inhomogeneous spatial point processes

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  • Yongtao Guan

Abstract

Summary. The paper introduces a new approach to estimate the variance of statistics that are computed from an inhomogeneous spatial point process. The approach proposed is based on the assumption that the observed point process can be thinned to be a second‐order stationary point process, where the thinning probability depends only on the first‐order intensity function of the (unthinned) original process. The resulting variance estimator is proved to be asymptotically consistent for the target parameter under some very mild conditions. The use of the approach proposed is demonstrated in two important applications of modelling inhomogeneous spatial point processes: residual diagnostics of a fitted model and inference on the unknown regression coefficients. A simulation study and an application to a real data example are used to demonstrate the efficacy of the approach proposed.

Suggested Citation

  • Yongtao Guan, 2008. "Variance estimation for statistics computed from inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 175-190, February.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:1:p:175-190
    DOI: 10.1111/j.1467-9868.2007.00632.x
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    References listed on IDEAS

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    1. Guan, Yongtao & Loh, Ji Meng, 2007. "A Thinned Block Bootstrap Variance Estimation Procedure for Inhomogeneous Spatial Point Patterns," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1377-1386, December.
    2. 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.
    3. Rasmus Plenge Waagepetersen, 2007. "An Estimating Function Approach to Inference for Inhomogeneous Neyman–Scott Processes," Biometrics, The International Biometric Society, vol. 63(1), pages 252-258, March.
    4. A. Baddeley & R. Turner & J. Møller & M. Hazelton, 2005. "Residual analysis for spatial point processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 617-666, November.
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