Testing first-order spherical symmetry of spatial point processes
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https://doi.org/10.5705/ss.202018.0214 |
Metadatos
Título
Testing first-order spherical symmetry of spatial point processesFecha de publicación
2020Editor
Institute of Statistical Science, Academia Sinica & International Chinese Statistical AssociationISSN
1017-0405Cita bibliográfica
Zhang, Tonglin, and Jorge Mateu. “Testing first-order spherical symmetry of spatial point processes.” Statistica Sinica, vol. 30, no. 3, 2020, pp. 1313–32.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www3.stat.sinica.edu.tw/statistica/J30N3/J30N38/J30N38.htmlVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
This study proposes a Kolmogorov-Smirnov-type test to assess the spherical symmetry of the first-order intensity function of a spatial point process (SPP). Spherical symmetry, which is an important assumption in the ... [+]
This study proposes a Kolmogorov-Smirnov-type test to assess the spherical symmetry of the first-order intensity function of a spatial point process (SPP). Spherical symmetry, which is an important assumption in the well known epidemic-type aftershock sequence (ETAS) model, means that the intensity function of an SPP is invariant under a spherical transformation in a Euclidean space. An important property of first-order spherical symmetry is that the expected number of points within a sector region is proportional to the angle measure of the region. This provides a way to construct our test statistic. The asymptotic distribution of the test statistic is obtained under the framework of increasing domain asymptotics, with weak dependence. We show that the resulting test statistic converges weakly to the absolute maximum of a zero mean Gaussian process under the null hypothesis, and that it is also consistent under the alternative hypothesis. A simulation study shows that the type-I error probability of the test is close to the significance level, and the power increases to one as the magnitude of nonspherical symmetry increases. An application of the ETAS model to earthquakes in Japan shows that the first-order spherical symmetry assumption can be approximately accepted. [-]
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Statistica Sinica, Vol. 30, No. 3 (2020)Derechos de acceso
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/restrictedAccess
info:eu-repo/semantics/restrictedAccess
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