A second-order test to detect spatio-temporal anisotropic effects in point patterns. Issue 4 (4th July 2018)

• Record Type: Journal Article
• Authors: Comas, C.; Conde, J.; Mateu, J.
• Is Part Of: Statistics. Volume 52:Issue 4(2018)
• Page Start: 717
• Page End: 733
• Publication Date: 2018-07-04
• Subjects: Anisotropy -- earthquakes -- K-function -- orientation distribution -- second-order intensity-reweighted -- space–time point patterns; 62M30; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1469633
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: 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, π ) 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.