Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Comparison of Two Proximity Catch Digraph Families in Testing Spatial
  Clustering   We consider two parametrized random digraph families, namely,
proportional-edge and central similarity proximity catch digraphs (PCDs) and
compare the performance of these two PCD families in testing spatial point
patterns. These PCD families are based on relative positions of data points
from two classes and the relative density of the PCDs is used as a statistic
for testing segregation and association against complete spatial randomness.
When scaled properly, the relative density of a PCD is a U-statistic. We extend
the distribution of the relative density of central similarity PCDs for
expansion parameter being larger than one. We compare the asymptotic
distribution of the statistic for the two PCD families, using the standard
central limit theory of U-statistics. We compare finite sample performance of
the tests by Monte Carlo simulations and prove the consistency of the tests
under the alternatives. The asymptotic performance of the tests under the
alternatives is assessed by Pitman's asymptotic efficiency. We find the optimal
expansion parameters of the PCDs for testing each of the segregation and
association alternatives in finite samples and in the limit. We demonstrate
that in terms of empirical power (i.e., for finite samples) relative density of
central similarity PCD has better performance (which occurs for expansion
parameter values larger than one) under segregation alternative, while relative
density of proportional-edge PCD has better performance under association
alternative. The methods are illustrated in a real-life example from plant
ecology.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an