  A new dimension reduction methodology 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, or jump, of functional means, leading to 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 throughly
developed 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 to the method based on functional principal components and
the fully functional approach without dimension reduction. An application to
annual humidity trajectories was also included to illustrate the practical
superiority of the developed approach.
