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A bootstrap test of independence between three temporal nonhomogeneous Poisson processes and its application to heat wave modeling

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Abstract

The main contribution of this work is a bootstrap test to check the independence between temporal nonhomogeneous Poisson processes. The test statistic is based on the close point relation, which adapts the crossed nearest neighbour distance ideas of spatial point processes to the case of nonhomogeneous time point processes. Since it is complicated to obtain the probability distribution of the test statistic under the null hypothesis and the parameters of the processes are usually unknown, the \(p\) value is obtained using a parametric bootstrap approach. A simulation study shows that the size of the test is close to the nominal one. The power is analyzed considering three approaches for generating dependent nonhomogeneous processes and different levels of dependence, and satisfactory results are obtained in all cases. Although the test was initially intended for Poisson processes, it can be applied to any type of point process in one dimension which can be simulated. This test is a valuable tool in the validation analysis of common Poisson shock models. For the bivariate case, the process can be decomposed into three independent Poisson processes, and the assumption of independence between them has to be checked. As an application, the joint modeling of the occurrence process of extreme heat events in daily maximum and minimum temperatures is described.

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Acknowledgments

This work was partially supported by Ministerio de Educación y Ciencia (Spanish Department of Science) and Ministerio de Medio Ambiente (Spanish Department of Environment) through the projects CGL2009-09646 and ESTCENA 2009/0017. We also thank the anonymous reviewers and the editors for their helpful comments.

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Authors and Affiliations

  1. Dpto. Métodos Estadísticos, Universidad de Zaragoza, Ed. Matemáticas, C\Pedro Cerbuna, 12, 50009 , Saragossa, Spain

    Jesús Abaurrea & Ana C. Cebrián

  2. Dpto. Métodos Estadísticos, Universidad de Zaragoza, EINA, C\María de Luna, 3, 50018 , Saragossa, Spain

    Jesús Asín

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  1. Jesús Abaurrea
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  2. Jesús Asín
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  3. Ana C. Cebrián
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Correspondence to Ana C. Cebrián.

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Handling Editor: Pierre Dutilleul.

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Abaurrea, J., Asín, J. & Cebrián, A.C. A bootstrap test of independence between three temporal nonhomogeneous Poisson processes and its application to heat wave modeling. Environ Ecol Stat 22, 127–144 (2015). https://doi.org/10.1007/s10651-014-0288-1

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  • DOI: https://doi.org/10.1007/s10651-014-0288-1

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