Mark distance correlation functions: from moment-based to distributional mark summary characteristics in spatial point processes

Abstract: With the rapid advancement in data collection devices and storage capacities, we have access to increasing amount of spatial point pattern data where each event location is augmented by multiple, potentially non-scalar marks. Therefore, there is need for efficient analysis techniques to investigate the structural relationships between the marks. In this paper, we recall the distance covariance and distance correlation and adjust them to the marked point process setting. As a result, we introduce a novel class of mark characteristics for single real-valued marks as well as multivariate combinations of marks, including mixtures of integer- and real-valued quantities, and non-scalar marks.