The asymptotic distribution of a cluster-index for i.i.d. normal random variables

Abstract

In a sample variance decomposition, with components functions of the sample's spacings, the largest component ${\tilde{I}}_n$ is used in cluster detection. It is shown for normal samples that the asymptotic distribution of ${\tilde{I}}_n$ is the Gumbel distribution.

Published in at http://dx.doi.org/10.1214/08-AAP553 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)