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Second-order analysis of anisotropic spatiotemporal point process data

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  • C. Comas
  • F. J. Rodriguez-Cortes
  • J. Mateu

Abstract

type="main" xml:id="stan12046-abs-0001"> Second-order orientation methods provide a natural tool for the analysis of spatial point process data. In this paper, we extend to the spatiotemporal setting the spatial point pair orientation distribution function. The new space–time orientation distribution function is used to detect space–time anisotropic configurations. An edge-corrected estimator is defined and illustrated through a simulation study. We apply the resulting estimator to data on the spatiotemporal distribution of fire ignition events caused by humans in a square area of 30 × 30 km-super-2 for 4 years. Our results confirm that our approach is able to detect directional components at distinct spatiotemporal scales. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.

Suggested Citation

  • C. Comas & F. J. Rodriguez-Cortes & J. Mateu, 2015. "Second-order analysis of anisotropic spatiotemporal point process data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 49-66, February.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:1:p:49-66
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    File URL: http://hdl.handle.net/10.1111/stan.12046
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    References listed on IDEAS

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    1. Yongtao Guan & Michael Sherman & James A. Calvin, 2006. "Assessing Isotropy for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 62(1), pages 119-125, March.
    2. Edith Gabriel & Peter J. Diggle, 2009. "Second‐order analysis of inhomogeneous spatio‐temporal point process data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(1), pages 43-51, February.
    3. Yongtao Guan & Michael Sherman & James A. Calvin, 2004. "A Nonparametric Test for Spatial Isotropy Using Subsampling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 810-821, January.
    4. Claudia Redenbach & Aila Särkkä & Johannes Freitag & Katja Schladitz, 2009. "Anisotropy analysis of pressed point processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(3), pages 237-261, September.
    5. 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.
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