Summary characteristics for multivariate function-valued spatial point process attributes

TL;DR

This paper extends existing spatial point process analysis methods to handle multivariate function-valued attributes, enabling more flexible analysis of complex spatial data with functional marks.

Contribution

It introduces a new framework for analyzing points with multivariate function-valued marks, including novel summary characteristics and estimators for such data.

Findings

Developed cross-function summary characteristics for multivariate functional marks.

Analyzed estimator behavior through simulations and real data applications.

Enhanced tools for modern spatial data analysis with complex functional attributes.

Abstract

Prompted 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.