Enhanced Change-Point Detection in Functional Means

Abstract

A new dimension reduction method for change-point detection in functional means is developed in this paper. The major advantage and novelty of the proposed method is its efficiency in selecting basis functions that capture the change/jump of functional means, leading to a higher detection power, especially when the functions cannot be sufficiently explained by a small number of basis functions or are contaminated by random noises. The theoretical results demonstrate that even when the change shrinks to zero, the proposed approach can still detect the change asymptotically almost surely. The numerical simulation studies justify the superiority of the proposed approach compared to the method based on functional principal components and the fully functional approach without dimension reduction. An application to annual humidity trajectories illustrates the practical superiority of the developed approach.