On using Reproducing Kernel Hilbert Spaces for the analysis of Replicated Spatial Point Processes

Abstract

This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel Hilbert Space and, as a result, methodological and theoretical results for statistical analysis in these spaces can be applied to them. In particular and by way of illustration, we show how we can use the proposed methodology to identify differences between several classes of replicated point patterns using the Box’s M and MANOVA tests, and to classify a new observation, using Discriminant Functions.