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Substationarity for spatial point processes

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  • Zhang, Tonglin
  • Mateu, Jorge

Abstract

This article aims to introduce the concept of substationarity for spatial point processes (SPPs). Substationarity is a new concept that has never been studied in the literature. Substationarity means that the distribution of an SPP can only be invariant under location shifts within a linear subspace of the domain. This notion lies theoretically between stationarity and nonstationarity. To formally propose the approach, the article provides the definition of substationarity and estimation of the first-order intensity function, including the subspace. As this may be unknown, we recommend using a parametric method to estimate the linear subspace and a nonparametric one to estimate the first-order intensity function given the linear subspace. It is thus a semiparametric approach. The simulation study shows that both the estimators of the linear subspace and the first-order intensity function are reliable. In an application to a Canadian forest wildfire data set, the article concludes that substationarity of wildfire occurrences may be assumed along the longitude, indicating that latitude is a more important factor than longitude in Canadian forest wildfire studies.

Suggested Citation

  • Zhang, Tonglin & Mateu, Jorge, 2019. "Substationarity for spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 22-36.
  • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:22-36
    DOI: 10.1016/j.jmva.2018.11.001
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    References listed on IDEAS

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