Cluster detection has become a vast field of statistics in the last decades. Among the known methods for detecting clusters, we can use the spatial scan statistics which are based on a collection of statistical tests. It allows to detect clusters in a geographical area. In a parametric way, scan statistics are defined from the likelihood ratio test and in the nonparametric way, they are constructed using the known nonparametric test statistic of Wilcoxon. In the literature, these techniques have been proposed and used in the univariate and the multivariate frameworks. In this talk, we introduce a nonparametric spatial scan statistic for functional data. It is derived from the Wilcoxon-Mann-Whitney statistic defined in infinite dimensional space. The proposed scan method is applied on simulated data for performance assessment, then on real data to extract characteristics of the demographic evolution of the Spanish population.
