Abstract

Detecting changes in functional data is a topic of great interest; however, it remains a challenging problem. Current approaches often rely on parametric assumptions about the data-generating process, making them sensitive to data contamination and assumption misspecification. This talk introduces two novel and robust nonparametric methods designed to overcome these challenges. We address the problem of detecting changepoints in both the location and variability of a sequence of independent multivariate functional observations.
First, we introduce the Functional Kruskal-Wallis for Covariance (FKWC) changepoint detection procedure, which leverages multivariate functional data depth. Second, we explore a graph-based changepoint detection method for identifying shifts in the mean function of the process. These methods have practical applications in various fields, and their effectiveness is demonstrated through several simulation studies.