标题： 增强的功能均值变化点检测 显示英文标题

标题： Enhanced Change-Point Detection in Functional Means

摘要： 本文提出了一种新的降维方法，用于检测函数均值中的变点。所提出方法的主要优势和创新之处在于其能够高效选择捕捉函数均值变化（或跳跃）的基函数，从而提高检测能力，特别是在函数不能由少量基函数充分解释或受到随机噪声污染的情况下。通过全面发展的理论结果表明，即使变点趋于零，所提出的方法仍可以渐近地几乎确定地检测到变点。数值模拟研究证明了所提出方法相对于基于函数主成分分析方法和无降维的完全函数方法的优势。此外，还包含了一项关于年湿度轨迹的应用，以展示所开发方法的实际优越性。 显示英文摘要

摘要： 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.