  We use the domination number of a parametrized random digraph family called
proportional-edge proximity catch digraphs (PCDs) for testing multivariate
spatial point patterns. This digraph family is based on relative positions of
data points from various classes. We extend the results on the distribution of
the domination number of proportional-edge PCDs, and use the domination number
as a statistic for testing segregation and association against complete spatial
randomness. We demonstrate that the domination number of the PCD has binomial
distribution when size of one class is fixed while the size of the other (whose
points constitute the vertices of the digraph) tends to infinity and asymptotic
normality when sizes of both classes tend to infinity. We evaluate the finite
sample performance of the test by Monte Carlo simulations, prove the
consistency of the test under the alternatives, and suggest corrections for the
support restriction on the class of points of interest and for small samples.
We find the optimal parameters for testing each of the segregation and
association alternatives. Furthermore, the methodology discussed in this
article is valid for data in higher dimensions also.
