Investigating spatial scan statistics for multivariate functional data

Abstract

In environmental surveillance, cluster detection of environmental black spots is of major interest due to the adverse health effects of pollutants, as well as their known synergistic effect. Thus, this paper introduces three new spatial scan statistics for multivariate functional data, applicable for detecting clusters of abnormal air pollutants concentrations measured spatially at a very fine scale in northern France in October 2021 taking into account their correlations. Mathematically, our methodology is derived from a functional multivariate analysis of variance, an adaptation of the Hotelling T2-test statistic, and a multivariate extension of the Wilcoxon test statistic. The approaches were evaluated in a simulation study and then applied to the air pollution dataset.