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.

翻译：本文件为功能性手段的改变点检测制定了一个新的减少维度的方法,主要优点和新颖之处是,拟议方法在选择基础功能性手段的改变或跳跃功能性功能方面的效率较高,从而导致更高的探测能力,特别是当这些功能不能由少量基础功能充分解释或受到随机噪音的污染时。通过发展的理论结果表明,即使这种改变缩小到零,拟议的方法仍然可以几乎肯定地不时地检测变化。数字模拟研究证明,基于功能性主要成分的拟议方法优于功能性主要成分,而完全功能性方法而不减少尺寸,具有优越性。还列入了对年度湿度轨迹的应用,以说明已开发方法的实际优越性。