The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association

Priebe et al. (2001. Statist. Prob. Lett. 55, 239-246) introduced the class cover catch digraphs and computed the distribution of the domination number of such digraphs for one-dimensional data. In higher dimensions these calculations are extremely difficult due to the geometry of the proximity regions; and only upper-bounds are available. In this article, we introduce a new type of data-random proximity map and the associated (di)graph in Rd. We find the asymptotic distribution of the domination number and use it for testing spatial point patterns of segregation and association.