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A general SLLN for the one-dimensional class cover problem

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  • Wierman, John C.
  • Xiang, Pengfei

Abstract

The class cover catch digraph (CCCD) is motivated by applications in statistical pattern classification. For the special case of uniformly distributed data in one dimension, Priebe et al. [Priebe, C.E., DeVinney, J.G., Marchette, D.J., 2001. On the distribution of the domination number for random class cover catch digraphs. Statist. Probab. Lett. 55, 239-246] found the exact distribution of the domination number of the random data-induced CCCD, and DeVinney and Wierman [DeVinney, J.G., Wierman, J.C., 2002. A SLLN for a one-dimensional class cover problem. Statist. Probab. Lett. 59, 425-435] proved the Strong Law of Large Numbers (SLLN). This paper proves the generalized SLLN for the domination number of CCCDs for non-uniform data in one dimension.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1110-1118
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. DeVinney, Jason & Wierman, John C., 2002. "A SLLN for a one-dimensional class cover problem," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 425-435, October.
    4. 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.
    5. 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. 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.
    2. 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.

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