The Asymptotic Distribution of a Cluster-index for I.i.d. Normal Random Variables
نویسندگان
چکیده
In a sample variance decomposition, with components functions of the sample's spacings, the largest component˜In is used in cluster detection. It is shown for normal samples that the asymptotic distribution of˜In is the Gumbel distribution. 1. Introduction. Clusters are nowadays data structures of considerable interest: Microarray data is used to attribute genes in clusters; gene expression is used to cluster tumors and identify similar types of cancer. Extreme value theory, in particular of sample spacings, has been used extensively in modeling phenomena. The extreme value˜I n of functions of spacings is introduced in Yatracos (2007) to detect data clusters from their one dimensional data projections; n is the size of the data. In this work, the asymptotic distribution of˜I n is obtained for data from the normal distribution, and can be used to determine statistical significance of potential clusters.
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