A general SLLN for the one-dimensional class cover problem

John C. Wierman and Pengfei Xiang

Statistics & Probability Letters, 2008, vol. 78, issue 9, 1110-1118

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.

Date: 2008
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