Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Family of Random Graphs for Testing Spatial Segregation   We discuss a graph-based approach for testing spatial point patterns. This
approach falls under the category of data-random graphs, which have been
introduced and used for statistical pattern recognition in recent years. Our
goal is to test complete spatial randomness against segregation and association
between two or more classes of points. To attain this goal, we use a particular
type of parametrized random digraph called proximity catch digraph (PCD) which
is based based on relative positions of the data points from various classes.
The statistic we employ is the relative density of the PCD. When scaled
properly, the relative density of the PCD is a $U$-statistic. We derive the
asymptotic distribution of the relative density, using the standard central
limit theory of $U$-statistics. The finite sample performance of the test
statistic is evaluated by Monte Carlo simulations, and the asymptotic
performance is assessed via Pitman's asymptotic efficiency, thereby yielding
the optimal parameters for testing. Furthermore, the methodology discussed in
this article is also valid for data in multiple dimensions.

31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas