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| 研究生： |
吳文瀚 Wen-han Wu |
|---|---|
| 論文名稱： |
函數資料之平均函數多重轉換點問題之探討 |
| 指導教授： |
丘政民
Jeng-Min Chiou |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 統計研究所 Graduate Institute of Statistics |
| 論文出版年： | 2014 |
| 畢業學年度： | 102 |
| 語文別： | 中文 |
| 論文頁數： | 36 |
| 中文關鍵詞： | 函數資料 、函數型主成份分析 、轉換點 |
| 外文關鍵詞： | functional data, FPCA, change point |
| 相關次數： | 點閱：9 下載：0 |
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本文探討函數資料在平均函數上具有多重轉換點之搜尋方法，轉換點問題的假設檢定根據對立假設的不同，例如AMOC假設、疫情假設，進而推導出檢定方法與轉換點的估計。本文考慮使用AMOC假設來建立轉換點搜尋法，想像透過一扇窗戶觀看函數資料，我們只能看到片段的資料。根據不同的窗戶大小及位置，所能看到的片段資料也會不同。透過改變這種窗戶的大小或位置，對一系列的片段資料做假設檢定，最後得到多重轉換點的搜尋結果，而不是一次性的對全部資料做假設檢定。此方法稱為開窗式搜尋法。本文利用模擬方法比較開窗式搜尋法與二分搜尋法的表現，雖然二分搜尋在理想上可以快速的找出所有轉換點，但模擬結果顯示出二分搜尋的表現較不佳；另一方面，開窗式搜尋雖然較費時，但有著較好的表現。
In this thesis, we compare two processes of detecting multiple changes in mean of functional data. Based on different alternative hypotheses, such as the AMOC alternative or the epidemic alternative, different hypothesis tests had been developed. We construct the detecting process based on the AMOC alternative. Imagine that there is a window which only contains a segment of the whole data. Different size or different location of the window makes the window contains different segment of the whole data. By changing the size or shift the location of the window, a sequence of segment data were tested for changes in mean. After the tests, we will have a result of the changes in mean of the whole data. This method is called the moving-window method. We compare it with the binary search by simulation. Ideally, the binary search could find all the changes quickly, but the simulation show a bad result. On the other hand, the moving-window method shows a better result but takes more time.
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