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On least squares fitting for stationary spatial point processes

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  • Yongtao Guan
  • Michael Sherman

Abstract

Summary. The K‐function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K‐function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through asymptotic theory, simulation experiments and an application to a data set on long leaf pine‐trees.

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  • 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.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:1:p:31-49
    DOI: 10.1111/j.1467-9868.2007.00575.x
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    Cited by:

    1. Yongtao Guan, 2011. "Second-Order Analysis of Semiparametric Recurrent Event Processes," Biometrics, The International Biometric Society, vol. 67(3), pages 730-739, September.
    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.
    4. Taylor, Benjamin M. & Davies, Tilman M. & Rowlingson, Barry S. & Diggle, Peter J., 2015. "Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i07).
    5. Jesper Møller & Carlos Díaz‐Avalos, 2010. "Structured Spatio‐Temporal Shot‐Noise Cox Point Process Models, with a View to Modelling Forest Fires," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 2-25, March.
    6. 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.
    7. Christophe Ange Napoléon Biscio & Frédéric Lavancier, 2017. "Contrast Estimation for Parametric Stationary Determinantal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 204-229, March.
    8. Tilman M. Davies & Martin L. Hazelton, 2013. "Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 355-389, November.
    9. Heinrich, Lothar, 2018. "Brillinger-mixing point processes need not to be ergodic," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 31-35.

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