透過限制性的最佳分割來檢測函數型資料中的多重轉折點

Detection of Multiple Changepoints in a Functional Data Sequence with Constrained Optimal Partitioning

蔡知諺(Chih-Yen Tsai)

指導教授 ： 陳裕庭

國立臺灣大學/理學院/統計與數據科學研究所/碩士(2024年)

https://doi.org/10.6342/NTU202402621

摘要

在本論文中，我們提出了一種針對函數型資料的多重轉折點懲罰估計方法。我們介紹一種多重轉折點檢測方法，並增強了懲罰函數。該方法可避免預先給定轉折點個數，使我們可以同時找轉折點的位置和個數。此外，為了避免發生任兩個連續轉折點過於接近，我們加入了一個限制式來解決此問題。我們使用兩種方法，信噪比和樣本分割來選擇最佳的懲罰參數。最後我們將我們的方法與其他方法比較，包括多重轉折點隔離（MCI）和二分法分割，且在一些常見情況下優於現存方法。

關鍵字

多重轉折點分析 ； 函數主成分分析 ； 弱相依性 ； 最優分割法 ； 信噪比 ； 樣本分割

並列摘要

In this thesis, we propose a method for penalized estimation of multiple changepoints in functional data sequences. We introduces a multiple changepoint detection method enhanced with a penalty function. This method eliminates the need to pre-specify the number of changepoints, enabling simultaneous detection of changepoint locations and quantities. Additionally, to mitigate the occurrence of overly close or consecutive changepoints, we introduce an additional constraint. We utilize two methods, the signal-to-noise ratio and sample splitting, to choose the optimal penalty parameter. Furthermore, we compare our method with others, including Multiple Changepoint Isolation (MCI) and the binary segmentation, demonstrating superior performance under some common scenarios.

並列關鍵字

Multiple changepoints ； Functional principal components ； Weak dependence ； Optimal partitioning ； Signal-to-noise ratio ； Sample splitting

參考文獻

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Berkes, I., Gabrys, R., Horváth, L., and Kokoszka, P. (2009). Detecting Changes in the Mean of Functional Observations. Journal of the Royal Statistical Society Series B: Statistical Methodology, 71(5):927–946.

Chen, Huang, T.-M., and Chiou, J.-M. (2023). Greedy segmentation for a functional data sequence. Journal of the American Statistical Association, 118(542):959–971.