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Testing separability in marked multidimensional point processes with covariates. (English) Zbl 1230.62110

Summary: In modeling marked point processes, it is convenient to assume a separable or multiplicative form for the conditional intensity, as this assumption typically allows one to estimate each component of the model individually. Tests have been proposed in the simple marked point process case, to investigate whether the mark distribution is separable from the spatial–temporal characteristics of the point process. We extend these tests to the case of a marked point process with covariates, and where one is interested in testing the separability of each of the covariates, as well as the marks and the coordinates of the point process. The extension is not at all trivial, and covariates must be treated in a fundamentally different way than marks and coordinates of the process, especially when the covariates are not uniformly distributed. An application is given to point process models for forecasting wildfire hazard in Los Angeles County, California, and solutions are proposed to the problem of how to proceed when the separability hypothesis is rejected.

MSC:

62M07 Non-Markovian processes: hypothesis testing
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62P12 Applications of statistics to environmental and related topics

Software:

sm; MASS (R); R
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Full Text: DOI

References:

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