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| Title: | 透過貪婪分割法偵測函數型資料序列的多重轉換點
Multiple changepoints detection for functional data sequence through greedy segmentation |
| Authors: | 陳裕庭
Chen, Yu-Ting |
| Contributors: | 黃子銘
丘政民
Huang, Tzee-Ming
Chiou, Jeng-Min
陳裕庭
Chen, Yu-Ting |
| Keywords: | 多重轉換點問題
函數型主成分分析
共變函數算子
假設檢定
Multiple changepoint problem
Functional principal component analysis
Covariance operator
Hypothesis testing |
| Date: | 2022 |
| Issue Date: | 2022-06-01 16:26:02 (UTC+8) |
| Abstract: | 在本研究中，我們針對函數型資料序列中的多重轉換點偵測問題提出了適當的準則，透過此準則可將多重轉換點視作該準則下的$M$維最佳分割。
但由於轉換點個數$M$為未知，在給定不同的$K$值的狀況下，我們進一步探討$K$維最佳分割與多重轉換點之間的關係，並且發現無論$K$相對於$M$大小，透過最佳分割作為轉換點的估計式皆展現了理論上的一致性。
其中，應用$K<M$時的結果，我們亦提出貪婪分割法來估計多重轉換點的位置；貪婪分割法不但擁有不亞於二元分割法的執行速度，且在不需要任何與至多一個轉換點相關的假設下依舊能保持理論上的一致性。
同時，基於貪婪分割法估計式，我們同時提出了與之相關的檢定統計量，透過該檢定統計量在不同情境下的漸近分布來估計轉換點的個數，並給出具體的演算法。
針對貪婪分割法在實務上的表現，我們透過一系列的模擬研究以及實例分析來加以驗證。
In this study, we propose a criterion for multiple changepoint detection in a functional data sequence.
Using the proposed criterion, the set of multiple changepoints can be characterized as an optimal $M$-segmentation.
However, because the number of changepoints $M$ is unknown, we further investigate the theoretical properties of the optimal $K$-segmentation with respect to different values of $K$. It turns out the optimal $K$-segmentation is always consistent no matter when $K\\geq M$ or when $K< M$.
Using the consistency result when $K< M$, we propose Greedy Segmentation estimator, which is as efficient as Binary Segmentation and holds the consistency property without any assumption related to the at-most-one-changepoint assumption. Meanwhile, we also propose a test statistic based on the Greedy Segmentation estimator, whose asymptotic distribution is helpful in estimating the number of changepoints $M$.
The whole procedure is integrated as an algorithm that is easy to apply.
Finally, we study the finite-sample performance of Greedy Segmentation algorithm through simulation study and data applications |
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| Description: | 博士
國立政治大學
統計學系
104354501 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0104354501 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202200419 |
| Appears in Collections: | [統計學系] 學位論文
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