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Second‐order analysis of marked inhomogeneous spatiotemporal point processes: Applications to earthquake data

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  • A. Iftimi
  • O. Cronie
  • F. Montes

Abstract

To analyze interactions in marked spatiotemporal point processes (MSTPPs), we introduce marked second‐order reduced moment measures and K‐functions for inhomogeneous second‐order intensity‐reweighted stationary MSTPPs. These summary statistics, which allow us to quantify dependence between different mark‐based classifications of points, depend on the specific mark space and mark reference measure chosen. Unbiased and consistent minus‐sampling estimators are derived for all statistics considered, and a test for random labeling is indicated. In addition, we treat Voronoi intensity estimators for MSTPPs. These new statistics are finally employed to analyze an Andaman Sea earthquake data set.

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  • A. Iftimi & O. Cronie & F. Montes, 2019. "Second‐order analysis of marked inhomogeneous spatiotemporal point processes: Applications to earthquake data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(3), pages 661-685, September.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:3:p:661-685
    DOI: 10.1111/sjos.12367
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    Cited by:

    1. Eckardt, Matthias & González, Jonatan A. & Mateu, Jorge, 2021. "Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. Mohammad Ghorbani & Ottmar Cronie & Jorge Mateu & Jun Yu, 2021. "Functional marked point processes: a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 529-568, September.

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