Scan Statistics for Detecting High-Variance Clusters

Scan statistics are mostly used to detect spatial areas or time intervals in which the mean level of a given variable is more important. Sometimes, when this variable is continuous, there is an interest in looking for clusters in which its variability is more important. In this paper, two scan statistics are introduced for identifying clusters of values exhibiting higher variance. Like many classical scan statistics, the first one relies on a generalized likelihood ratio test whereas the second one is based on ratios of empirical variances. These methods are useful to identify spatial areas or time intervals in which the variability of a given variable is more important. In an application of the new methods, I look for geographical clusters of high-variability income in France and then for residuals exhibiting higher variance in a linear regression context.