Investigating spatial scan statistics for multivariate functional data

TL;DR

This paper develops new spatial scan statistics for multivariate functional data, improving cluster detection accuracy and demonstrating effectiveness through simulations and real air pollution data analysis.

Contribution

Introduces novel spatial scan statistics based on MANOVA, Hotelling T2, and Wilcoxon tests for multivariate functional data, enhancing cluster detection accuracy.

Findings

Methods outperform existing nonparametric functional scan statistic.

Good performance of Hotelling T2 and Wilcoxon methods in simulations.

Effective detection of air pollution clusters in France.

Abstract

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.