  This paper introduces new scan statistics for multivariate functional data
indexed in space. The new methods are derivated from a MANOVA test statistic
for functional data, an adaptation of the Hotelling T2-test statistic, and a
multivariate extension of the Wilcoxon rank-sum test statistic. In a simulation
study, the latter two methods present very good performances and the adaptation
of the functional MANOVA also shows good performances for a normal
distribution. Our methods detect more accurate spatial clusters than an
existing nonparametric functional scan statistic. Lastly we applied the methods
on multivariate functional data to search for spatial clusters of abnormal
daily concentrations of air pollutants in the north of France in May and June
2020.
