Summary characteristics for multivariate function‐valued spatial point process attributes

Abstract

SummaryPrompted by modern technologies in data acquisition, the statistical analysis of spatially distributed function‐valued quantities has attracted a lot of attention in recent years. In particular, combinations of functional variables and spatial point processes yield a highly challenging instance of such modern spatial data applications. Indeed, the analysis of spatial random point configurations, where the point attributes themselves are functions rather than scalar‐valued quantities, is just in its infancy, and extensions to function‐valued quantities still remain limited. In this view, we extend current existing first‐ and second‐order summary characteristics for real‐valued point attributes to the case where, in addition to every spatial point location, a set of distinct function‐valued quantities are available. Providing a flexible treatment of more complex point process scenarios, we build a framework to consider points with multivariate function‐valued marks, and develop sets of different cross‐function (cross‐type and also multi‐function cross‐type) versions of summary characteristics that allow for the analysis of highly demanding modern spatial point process scenarios. We consider estimators of the theoretical tools and analyse their behaviour through a simulation study and two real data applications.