The distribution of the relative arc density of a family of interval catch digraph based on uniform data
We study a family of interval catch digraph called proportional-edge proximity catch digraph (PCD) which is also a special type of intersection digraphs parameterized with an expansion and a centrality parameter. PCDs are random catch digraphs that have been developed recently and have applications in classification and spatial pattern analysis. We investigate a graph invariant of the PCDs called relative arc density. We demonstrate that relative arc density of PCDs is a U-statistic and using the central limit theory of U-statistics, we derive the (asymptotic) distribution of the relative arc density of proportional-edge PCD for uniform data in one dimension. We also determine the parameters for which the rate of convergence to asymptotic normality is fastest. Copyright Springer-Verlag 2012
Volume (Year): 75 (2012)
Issue (Month): 6 (August)
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- Priebe, Carey E. & Solka, Jeffrey L. & Marchette, David J. & Clark, B. Ted, 2003. "Class cover catch digraphs for latent class discovery in gene expression monitoring by DNA microarrays," Computational Statistics & Data Analysis, Elsevier, vol. 43(4), pages 621-632, August.
- Ceyhan, Elvan & Priebe, Carey E., 2005. "The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 37-50, June.
- Priebe, Carey E. & DeVinney, Jason G. & Marchette, David J., 2001. "On the distribution of the domination number for random class cover catch digraphs," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 239-246, December.
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