Detecting change regions on spheres

TL;DR

This paper introduces CRISP, a novel estimator for detecting change regions on spheres, addressing the challenge of irregularly shaped spatial changes in manifold data, with proven convergence and real-world applications.

Contribution

The paper develops the CRISP estimator for change region detection on spheres, extending it to multiple regions and analyzing its convergence based on VC dimension, with practical demonstrations.

Findings

CRISP effectively detects change regions with promising finite-sample performance.

The convergence rate depends on the VC dimension of the hypothesis class.

Applications to temperature and ozone data demonstrate practical utility.

Abstract

While change point detection in time series data has been extensively studied, little attention has been given to its generalisation to data observed on spheres or other manifolds, where changes may occur within spatially complex regions with irregular boundaries, posing significant challenges. We propose a new class of estimators, namely, Change Region Identification and SeParation (CRISP), to locate changes in the mean function of a signal-plus-noise model defined on $d$-dimensional spheres. The CRISP estimator applies to scenarios with a single change region, and is extended to multiple change regions via a newly developed generic scheme. The convergence rate of the CRISP estimator is shown to depend on the VC dimension of the hypothesis class that characterises the change regions in general. We also carefully study the case where change regions have the geometry of spherical caps. Simulations confirm the promising finite-sample performance of this approach. The CRISP estimator's practical applicability is further demonstrated through two real data sets on global temperature and ozone hole.