Enhanced Structural Break Detection in Functional Means

A new change-point detector for structure breaks in functional means is developed in this paper. The detector is based on a novel easy-to-implement approach of dimension reduction. One major advantage of the proposed method is its efficiency in selecting the basis functions that capture the change/jump of functional means, leading to a higher detection power. We thoroughly investigate the asymptotic properties of the proposed detector when both the sample size and the incorporated dimension increase. The numerical simulation studies justify the superiority of the proposed approach compared to the existing competitors and highlight the necessity of aligning the basis functions with the change to be detected. An application to annual humidity trajectories illustrates the practical superiority of the developed approach.