论文标题
部分可观测时空混沌系统的无模型预测
Enhanced Change-Point Detection in Functional Means
论文作者
论文摘要
在本文中开发了一种新的降低尺寸方法，用于功能手段中的变更点检测。该方法的主要优势和新颖性是它在选择捕获功能手段变化或跳跃的基础函数方面的效率，从而导致更高的检测能力，尤其是当函数无法充分解释功能时，少量基础函数或被随机声音污染时。漫步的理论结果表明，即使变化缩小到零，提出的方法仍然可以肯定地渐近地检测到变化。数值仿真研究证明了基于功能主成分和完全功能的方法而没有降低尺寸的方法对方法的优越性。还包括对年度湿度轨迹的应用，以说明开发方法的实际优势。
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.
