The Use of Domination Number of a Random Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association

Details The Use of Domination Number of a Random Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association The Use of Domination Number of a Random Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association

2008-02-05

arxiv.org/abs/0802.0638v1

Statistics & Probability Letters (2005), 73, 37-50

Statistics

Methodology

13 pages, 7 figures

Scientific paper

Priebe et al. (2001) 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 $\mathbb R^d$. We find the asymptotic distribution of the domination number and use it for testing spatial point patterns of segregation and association.

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