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The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association

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  • Ceyhan, Elvan
  • Priebe, Carey E.

Abstract

Priebe et al. (2001. Statist. Prob. Lett. 55, 239-246) 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 . We find the asymptotic distribution of the domination number and use it for testing spatial point patterns of segregation and association.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:1:p:37-50
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Elvan Ceyhan, 2012. "The distribution of the relative arc density of a family of interval catch digraph based on uniform data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 761-793, August.
    2. Wierman, John C. & Xiang, Pengfei, 2008. "A general SLLN for the one-dimensional class cover problem," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1110-1118, July.
    3. Xiang, Pengfei & Wierman, John C., 2009. "A CLT for a one-dimensional class cover problem," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 223-233, January.
    4. Elvan Ceyhan, 2012. "An Investigation of New Graph Invariants Related to the Domination Number of Random Proximity Catch Digraphs," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 299-334, June.
    5. Ceyhan, Elvan & Priebe, Carey E. & Wierman, John C., 2006. "Relative density of the random r-factor proximity catch digraph for testing spatial patterns of segregation and association," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1925-1964, April.

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    1. Ceyhan, Elvan & Priebe, Carey E. & Wierman, John C., 2006. "Relative density of the random r-factor proximity catch digraph for testing spatial patterns of segregation and association," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1925-1964, April.
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