Test for independence between marks and points of marked point processes: A subsampling approach

Ecological data often involve measurements taken at irregularly spaced locations (e.g., the heights of trees in a forest). A useful approach for modeling such data is via a marked point process, where the marks (i.e., measurements) and points (i.e., locations) are often assumed to be independent. Although this is a convenient assumption, it may not hold in practice. Schlather et al. (Journal of the Royal Statistical Society Services B, 66, 79-93, 2004) proposed a simulation-based approach to test this assumption. This paper presents a new method for testing the assumption of independence between the marks and the points. Instead of considering a simulation approach, we derive analytical results that allow the test to be implemented via a conventional χ² statistic. We illustrate the use of our approach by applying it to an example involving desert plant data.