使用資料深度來識別各種函數型資料的變化

Abstract

在函數型資料中的轉折點檢測方法引起了廣泛關注並持續發展，從早期的``CUSUM" 衍生到越來越複雜的損失函數。而先前的方法往往需仰賴動差估計量，對於函數型資料來說既耗時且實用性也較低。為了提高研究方法的可行性，本篇提出利用資料深度來建立一個統計量並將其應用在判定轉折點發生位置，最後再結合樣本分割的方法來確認數據中是否確實發生變化。文章後續的模擬也演示了我們方法的可行性，並突顯了不同參數設置的影響。且在文章的最後，我們會針對研究結果做簡單總結並提出一些可改進的方向。

Methods for change-point detection in functional data have garnered significant attention and continue to evolve, from the early derivation of ``CUSUM" to the emergence of increasingly complex loss functions. However, previous methods often rely on moment estimators which may be time-consuming and impractical for functional data, especially in estimating higher-order moments. To enhance the feasibility, we propose utilizing data depth to establish a statistical measure for identifying change point locations and combine this statistic with the sample splitting method to confirm whether a change has truly occurred in the data. The simulation results demonstrate the feasibility of our method and highlight the impact of different parameter settings. In the conclusion, we provide a summary of our findings and suggest potential directions for future improvements.