Summary characteristics for multivariate function-valued spatial point process attributes
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 s...
| Authors: | ; ; |
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| Format: | Article |
| Status: | Published version |
| Publication date: | 2025 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/466309 |
| Online Access: | https://doi.org/10.1111/insr.12582 https://hdl.handle.net/10459.1/466309 |
| Access Level: | Open access |
| Keyword: | Cross-function mark correlation Forest monitoring data Functional-marked point processes Mark variogram Mark weighted second order summary characteristics |
| Summary: | 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. |
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