請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/95725完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳裕庭 | zh_TW |
| dc.contributor.advisor | Yu-Ting Chen | en |
| dc.contributor.author | 吳維哲 | zh_TW |
| dc.contributor.author | Wei-Che Wu | en |
| dc.date.accessioned | 2024-09-15T17:00:52Z | - |
| dc.date.available | 2024-09-16 | - |
| dc.date.copyright | 2024-09-15 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-08-09 | - |
| dc.identifier.citation | Elena Andreou and Eric Ghysels. Detecting multiple breaks in financial market volatility dynamics. Journal of applied Econometrics, 17(5):579–600, 2002.
John AD Aston and Claudia Kirch. Detecting and estimating changes in dependent functional data. Journal of Multivariate Analysis, 109:204–220, 2012. John AD Aston, Davide Pigoli, and Shahin Tavakoli. Tests for separability in nonparametric covariance operators of random surfaces. The Annals of Statistics, pages 1431–1461, 2017. Alexander Aue, Robertas Gabrys, Lajos Horváth, and Piotr Kokoszka. Estimation of a change-point in the mean function of functional data. Journal of Multivariate Analysis, 100(10):2254–2269, 2009. Alexander Aue, Gregory Rice, and Ozan Sönmez. Detecting and dating structural breaks in functional data without dimension reduction. Journal of the Royal Statistical Society Series B: Statistical Methodology, 80(3):509–529, 2018. Alexander Aue, Gregory Rice, and Ozan Sönmez. Structural break analysis for spectrum and trace of covariance operators. Environmetrics, 31(1):e2617, 2020. Claudie Beaulieu, Jie Chen, and Jorge L Sarmiento. Change-point analysis as a tool to detect abrupt climate variations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 370(1962):1228–1249, 2012. István Berkes, Robertas Gabrys, Lajos Horváth, and Piotr Kokoszka. Detecting changes in the mean of functional observations. Journal of the Royal Statistical Society Series B: Statistical Methodology, 71(5):927–946, 2009. Shojaeddin Chenouri, Ahmad Mozaffari, and Gregory Rice. Robust multivariate change point analysis based on data depth. Canadian Journal of Statistics, 48(3):417–446, 2020. Jeng-Min Chiou, Yu-Ting Chen, and Tailen Hsing. Identifying multiple changes for a functional data sequence with application to freeway traffic segmentation. The Annals of Applied Statistics, 13(3):1430–1463, 2019. Terence Tai-Leung Chong. Estimating the locations and number of change points by the sample-splitting method. Statistical papers, 42:53–79, 2001. Antonio Cuevas, Manuel Febrero, and Ricardo Fraiman. On the use of the bootstrap for estimating functions with functional data. Computational statistics & data analysis, 51(2):1063–1074, 2006. Antonio Cuevas, Manuel Febrero, and Ricardo Fraiman. Robust estimation and classification for functional data via projection-based depth notions. Computational Statistics, 22(3):481–496, 2007. Holger Dette and Kevin Kokot. Detecting relevant differences in the covariance operators of functional time series: a sup-norm approach. Annals of the Institute of Statistical Mathematics, 74(2):195–231, 2022. Ricardo Fraiman and Graciela Muniz. Trimmed means for functional data. Test, 10: 419–440, 2001. Oleksandr Gromenko, Piotr Kokoszka, and Matthew Reimherr. Detection of change in the spatiotemporal mean function. Journal of the Royal Statistical Society Series B: Statistical Methodology, 79(1):29–50, 2017. Trevor Harris, Bo Li, and J Derek Tucker. Scalable multiple changepoint detection for functional data sequences. Environmetrics, 33(2):e2710, 2022. Siegfried Hörmann and Piotr Kokoszka. Weakly dependent functional data. 2010. Lajos Horváth and Marie Hušková. Change-point detection in panel data. Journal of Time Series Analysis, 33(4):631–648, 2012. Huang Huang and Ying Sun. A decomposition of total variation depth for understanding functional outliers. Technometrics, 2019. Daniela Jarušková. Testing for a change in covariance operator. Journal of Statistical Planning and Inference, 143(9):1500–1511, 2013. Shuhao Jiao, Ron D Frostig, and Hernando Ombao. Break point detection for functional covariance. Scandinavian Journal of Statistics, 50(2):477–512, 2023. Tze Leung Lai. Sequential changepoint detection in quality control and dynamical systems. Journal of the Royal Statistical Society: Series B (Methodological), 57(4):613–644, 1995. Jun Li and Regina Y Liu. New nonparametric tests of multivariate locations and scales using data depth. 2004. Regina Y Liu. On a notion of data depth based on random simplices. The Annals of Statistics, pages 405–414, 1990. Regina Y Liu, Jesse M Parelius, and Kesar Singh. Multivariate analysis by data depth: descriptive statistics, graphics and inference,(with discussion and a rejoinder by liu and singh). The annals of statistics, 27(3):783–858, 1999. Sara López-Pintado and Juan Romo. On the concept of depth for functional data. Journal of the American statistical Association, 104(486):718–734, 2009. Karl Mosler. Depth statistics. Robustness and complex data structures: Festschrift in Honour of Ursula Gather, pages 17–34, 2013. Vito MR Muggeo and Giada Adelfio. Efficient change point detection for genomic sequences of continuous measurements. Bioinformatics, 27(2):161–166, 2011. Yue S Niu and Heping Zhang. The screening and ranking algorithm to detect dna copy number variations. The annals of applied statistics, 6(3):1306, 2012. James O Ramsay and Bernard W Silverman. Fitting differential equations to functional data: Principal differential analysis. Springer, 2005. Kelly Ramsay and Shoja’eddin Chenouri. Change-point detection in the covariance kernel of functional data using data depth. arXiv preprint arXiv:2112.01611, 2021. Shawn Santo and Ping-Shou Zhong. Homogeneity tests of covariance and change-points identification for high-dimensional functional data. arXiv preprint arXiv:2005.01895, 2020. Changliang Zou, Guanghui Wang, and Runze Li. Consistent selection of the number of change-points via sample-splitting. Annals of statistics, 48(1):413, 2020. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/95725 | - |
| dc.description.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。 | zh_TW |
| dc.description.abstract | 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. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-09-15T17:00:52Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-09-15T17:00:52Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Acknowledgments i
摘要 iii Abstract v Contents vii Chapter 1 Introduction 1 Chapter 2 Data Depth and Methodology 5 2.1 Review of Functional Data Depth 6 2.1.1 FM-depth 6 2.1.2 Random projection depth 7 2.1.3 Band depth and modified band depth 8 2.2 Method Proposed 10 2.3 Remarks on proposed method 15 Chapter 3 Simulation Study 17 3.1 Simulation setting 17 3.2 Comparison 19 3.3 Window Size Decision 25 Chapter 4 Summary and Discussion 29 References 31 | - |
| dc.language.iso | en | - |
| dc.title | 使用資料深度來識別各種函數型資料的變化 | zh_TW |
| dc.title | Identification of various functional changes with the aid of data depth | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 楊鈞澔;李百靈 | zh_TW |
| dc.contributor.oralexamcommittee | Chun-Hao Yang;Pai-Ling Li | en |
| dc.subject.keyword | 函數型資料,資料深度,轉折點分析,CUSUM,樣本分割, | zh_TW |
| dc.subject.keyword | Functional Data,Data Depth,Change-Point Analysis,CUSUM,Sample Splitting, | en |
| dc.relation.page | 34 | - |
| dc.identifier.doi | 10.6342/NTU202402805 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-08-12 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 統計與數據科學研究所 | - |
| 顯示於系所單位： | 統計與數據科學研究所 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-112-2.pdf | 859.34 kB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。