Detecting spatial clusters in functional data: new scan statistic approaches

TL;DR

This paper introduces two novel scan statistics for detecting spatial clusters in functional data, demonstrating improved detection of smaller clusters and better performance in simulations and real-world unemployment data analysis.

Contribution

The paper presents two new spatial scan statistic methods for functional data, including a distribution-free approach and an adapted ANOVA-based method, enhancing cluster detection capabilities.

Findings

Distribution-free method outperforms nonparametric functional scan statistic in simulations.

ANOVA-based method performs better with normal or quasi-normal data.

Methods successfully identified spatial clusters of unemployment in France.

Abstract

We have developed two scan statistics for detecting clusters of functional data indexed in space. The first method is based on an adaptation of a functional analysis of variance and the second one is based on a distribution-free spatial scan statistic for univariate data. In a simulation study, the distribution-free method always performed better than a nonparametric functional scan statistic, and the adaptation of the anova also performed better for data with a normal or a quasi-normal distribution. Our methods can detect smaller spatial clusters than the nonparametric method. Lastly, we used our scan statistics for functional data to search for spatial clusters of abnormal unemployment rates in France over the period 1998-2013 (divided into quarters).