A second-order test to detect spatio-temporal anisotropic effects in point patterns. (English) Zbl 1440.62342
Summary: Second-order spatio-temporal orientation methods provide a natural tool for the analysis of anisotropic spatio-temporal point process data. In this paper, we generalize a method based on the spatial point pair orientation distribution function to test for evidence of spatio-temporal anisotropy, by exploring the fact that the space-time orientation function is the distribution function of a uniform random variable on \([0,\pi)\) for any second-order intensity reweighted stationary and isotropic spatio-temporal point process. We present a numerical procedure based on this result to test for anisotropic effects, illustrated through a simulation study considering several space-time structures including Poisson and cluster configurations. The resulting testing procedure is applied to analyse the spatio-temporal distribution of earthquakes in Southern California for the period 1984–2004. Our results confirm that our approach is able to detect directional components at distinct spatio-temporal scales.
MSC:
| 62M30 | Inference from spatial processes |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 62P12 | Applications of statistics to environmental and related topics |
Keywords:
anisotropy; earthquakes; \(K\)-function; orientation distribution; second-order intensity-reweighted; space-time point patternsSoftware:
k.cReferences:
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