Second‐order analysis of marked inhomogeneous spatiotemporal point processes: Applications to earthquake data

A. Iftimi, O. Cronie and F. Montes

Scandinavian Journal of Statistics, 2019, vol. 46, issue 3, 661-685

Abstract: To analyze interactions in marked spatiotemporal point processes (MSTPPs), we introduce marked second‐order reduced moment measures and K‐functions for inhomogeneous second‐order intensity‐reweighted stationary MSTPPs. These summary statistics, which allow us to quantify dependence between different mark‐based classifications of points, depend on the specific mark space and mark reference measure chosen. Unbiased and consistent minus‐sampling estimators are derived for all statistics considered, and a test for random labeling is indicated. In addition, we treat Voronoi intensity estimators for MSTPPs. These new statistics are finally employed to analyze an Andaman Sea earthquake data set.

Date: 2019
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