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.

翻译：本文件介绍了空间指数化多变量功能数据的新扫描统计数据,新方法来自MANOVA功能数据测试统计数据、Hontling T2-Test统计数据的修改以及Wilcoxon级和测试统计数据的多变量扩展。在模拟研究中,后两种方法表现良好,功能性MONOVA也显示正常分布的性能良好。我们的方法探测到的空间集群比现有的非参数性功能扫描统计数据更准确。最后,我们于2020年5月和6月在法国北部应用了多变量功能数据方法搜索每日异常空气污染物浓度的空间集群。