Change region detection on d-dimensional spheres

Change point detection in time series data has been extensively studied, but little attention has been given to its generalization to higher dimensional spaces, where changes may occur in different regions with irregular boundaries, posing significant challenges. This talk introduces a method to locate changes in the mean function of a signal-plus-noise model on d-dimensional spheres. We find that the convergence rate depends on the VC dimension of the hypothesis class that characterizes the underlying change regions. Our results extend to data lying on manifolds, under the assumption of a single change region. Furthermore, we adapt the method to address scenarios with multiple change regions. Simulation studies confirm the consistency of our approach for both single and multiple change scenarios with varying mean values across regions.