Nonparametric spatial scan statistics for real and functional data

Abstract

Cluster detection has become a vast field of statistics in the last decades. These techniques have applications in various fields: epidemiology, environmental sciences, socioeconomic, etc. 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, after a pedagogical introduction to the subject, we present a nonparametric spatial scan method for functional data. The associated scan statistic is derived from the Wilcoxon-Mann-Whitney test statistic defined for infinite dimensional data. It is completely nonparametric as it does not assume any distribution concerning the functional marks. In our simulation study, this scan test appears to be powerful against clustering alternatives based on other scan statistics. We also apply our method to a data set for extracting features in Spanish province population growth. A significant and relevant spatial cluster with a low rate of demographic change is found in North-West of Spain.