Change-point Detection for Sparse and Dense Functional Data in General Dimensions

We study the problem of change-point detection and localisation for functional data sequentially observed on a general d -dimensional space, where we allow the functional curves to be either sparsely or densely sampled. Data of this form naturally arise in a wide range of applications such as biology, neuroscience, climatology and finance. To achieve such a task, we propose a kernel-based algorithm named functional seeded binary segmentation (FSBS). FSBS is computationally efficient, can handle discretely observed functional data, and is theoretically sound for heavy-tailed and temporally-dependent observations. Moreover, FSBS works for a general d -dimensional domain, which is the first in the literature of change-point estimation for functional data.