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Similarity measures of conditional intensity functions to test separability in multidimensional point processes

Stochastic Environmental Research and Risk Assessment volume 27, pages 1193–1205 (2013)Cite this article

Abstract

Separability in the context of multidimensional point processes assumes a multiplicative form for the conditional intensity function. This hypothesis is especially convenient since each component of a separable process may be modeled and estimated individually, and this greatly facilitates model building, fitting, and assessment. This is also related to the problem of reduction in the number of dimensions. Following previous approximations to this problem, we focus on the conditional intensity function, by considering nonparametric kernel-based estimators. Our approach calculates thinning probabilities under the conditions of separability and nonseparability and compares them through divergence measures. Based on Monte Carlo experiments, we approximate the statistical properties of our tests under a variety of practical scenarios. An application on modeling the spatio-temporal first-order intensity of forest fires is also developed.

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Acknowledgements

Work partially funded by Grant MTM2010-14961 from the Spanish Ministry of Science and Education, and by the program PASPA of the Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México.

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Authors and Affiliations

  1. Research Institute in Applied Mathematics and Systems, National University of Mexico, Mexico, DF, Mexico

    Carlos Díaz-Avalos

  2. Department of Mathematics, Universitat Jaume I, Campus Riu Sec, 12071, Castellón, Spain

    P. Juan & J. Mateu

Authors
  1. Carlos Díaz-Avalos
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  2. P. Juan
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  3. J. Mateu
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Correspondence to Carlos Díaz-Avalos.

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Díaz-Avalos, C., Juan, P. & Mateu, J. Similarity measures of conditional intensity functions to test separability in multidimensional point processes. Stoch Environ Res Risk Assess 27, 1193–1205 (2013). https://doi.org/10.1007/s00477-012-0654-1

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  • DOI: https://doi.org/10.1007/s00477-012-0654-1

Keywords

  • Conditional intensity function
  • Covariates
  • Multidimensional spatial point processes
  • Nonparametric estimation
  • Separability
  • Wildfires

Mathematics Subject Classifications

  • 62H10
  • 62H15