Testing the random field model hypothesis for random marked closed sets

When developing statistical models, it is of fundamental importance to decide if the various components are independent of one another, preferably using a formal statistical test. Non-parametric versions of such tests are particularly useful, as they do not require extensive a priori   knowledge about the underlying models. In this paper, we develop such tests for random marked closed sets, which have many applications in spatial statistics. More precisely, we investigate two approaches to testing if the marks are independent of the closed set. Both approaches are based on second-order characteristics of random marked closed sets. The first approach uses a global rank envelope test based on the mark-weighted KK-function. The second approach uses an asymptotic test developed for marked point processes. We carry out extensive simulation studies to assess the performance of these tests, demonstrating that the global rank envelope test is a better choice. Finally, we apply this test to two real world data sets.