# Investigating spatial scan statistics for multivariate functional data

**Authors:** Camille Frévent, Mohamed-Salem Ahmed, Sophie Dabo-Niang, Michaël Genin  
**arXiv:** [2103.14401](https://arxiv.org/abs/2103.14401)  
**Date:** 2021-03-26  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2103.14401v1/

## Key points

- Introduction of innovative scan statistics for multivariate functional data indexed in space
- Derived from MANOVA test statistic, adaptation of Hotelling T2-test statistic, and multivariate extension of Wilcoxon rank-sum test statistic
- Exceptional performance of Hotelling T2-test and Wilcoxon rank-sum test methods
- Strong results for functional MANOVA on normal distribution datasets
- Comparison with existing nonparametric functional scan statistic:
- Newly proposed methods more effective in detecting spatial clusters
- Practical application on abnormal air pollutant concentrations in northern France during May and June 2020:
- Utilization of novel scan statistics to identify spatial patterns
- Contribution to spatial statistics field by offering advanced tools for analyzing multivariate functional data indexed in space:
- Enhancing understanding of spatial clustering
- Providing insights for addressing environmental challenges like air pollution monitoring and management

## Summary

The research introduces innovative scan statistics tailored for multivariate functional data indexed in space. These new methods are derived 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. Through a comprehensive simulation study, the authors demonstrate that the latter two methods exhibit exceptional performance. Additionally, the adaptation of the functional MANOVA also showcases strong results when applied to datasets following a normal distribution. Compared to an existing nonparametric functional scan statistic, the newly proposed methods prove to be more effective in accurately detecting spatial clusters. In a practical application of their methodology, the researchers utilize these novel scan statistics on multivariate functional data to investigate spatial clusters of abnormal daily concentrations of air pollutants in northern France during May and June 2020. This real-world application underscores the relevance and utility of their proposed techniques in identifying and analyzing spatial patterns within complex datasets. Overall, this study contributes significantly to the field of spatial statistics by offering advanced tools for analyzing multivariate functional data indexed in space. The findings not only enhance our understanding of spatial clustering but also provide valuable insights for addressing environmental challenges such as air pollution monitoring and management.