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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 丘政民 | zh_TW |
dc.contributor.advisor | Jeng-Min Chiou | en |
dc.contributor.author | 陳文凱 | zh_TW |
dc.contributor.author | Wen-Kai Chen | en |
dc.date.accessioned | 2024-08-05T16:24:32Z | - |
dc.date.available | 2024-08-06 | - |
dc.date.copyright | 2024-08-05 | - |
dc.date.issued | 2024 | - |
dc.date.submitted | 2024-07-27 | - |
dc.identifier.citation | Abramowicz, K., Pini, A., Schelin, L., Sjöstedt de Luna, S., Stamm, A., and Vantini, S. (2023). Domain selection and familywise error rate for functional data: A unified framework. Biometrics, 79(2):1119–1132.
Chiou, J.M. (2012). Dynamical functional prediction and classification, with application to traffic flow prediction. The Annals of Applied Statistics, 6(4):1588 – 1614. Cuevas, A., Febrero, M., and Fraiman, R. (2004). An anova test for functional data. Computational statistics & data analysis, 47(1):111–122. Fan, J. and Gijbels, I. (1996). Local polynomial modelling and its applications. Fremdt, S., Steinebach, J. G., Horváth, L., and Kokoszka, P. (2013). Testing the equal ity of covariance operators in functional samples. Scandinavian Journal of Statistics, 40(1):138–152. Hochberg, Y. (1987). Multiple comparison procedures. Wiley Series in Probability and Statistics. Hsing, T. and Eubank, R. (2015). Theoretical foundations of functional data analysis, with an introduction to linear operators, volume 997. John Wiley & Sons. Pesarin, F. and Salmaso, L. (2010). Permutation tests for complex data: theory, applica tions and software. John Wiley & Sons. Pigoli, D., Aston, J. A., Dryden, I. L., and Secchi, P. (2014). Distances and inference for covariance operators. Biometrika, 101(2):409–422. Pilavakis, D., Paparoditis, E., and Sapatinas, T. (2020). Testing equality of autocovariance operators for functional time series. Journal of Time Series Analysis, 41(4):571–589. Pini, A. and Vantini, S. (2016). The interval testing procedure: a general framework for inference in functional data analysis. Biometrics, 72(3):835–845. Pini, A. and Vantini, S. (2017). Intervalwise testing for functional data. Journal of Non parametric Statistics, 29(2):407–424. Ramsay, J. and Silverman, B. (2005). Functional Data Analysis. Springer Series in Statis tics. Springer. Ramsay, J. O. (1982). When the data are functions. Psychometrika, 47:379–396. Vsevolozhskaya, O., Greenwood, M., and Holodov, D. (2014). Pairwise comparison of treatment levels in functional analysis of variance with application to erythrocyte hemolysis. The Annals of Applied Statistics, 8(2):905 – 925. Wang, J.L., Chiou, J.M., and Müller, H.G. (2016). Functional data analysis. Annual Review of Statistics and its application, 3:257–295. Yao, F., Müller, H.G., and Wang, J.L. (2005). Functional data analysis for sparse longi tudinal data. Journal of the American statistical association, 100(470):577–590. Zhang, J. (2014). Analysis of variance for functional data. Monographs on statistics and applied probability, 127:127. | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93534 | - |
dc.description.abstract | 在函數數據的雙樣本檢定中,我們除了判定樣本的差異與否,還特別關注差異的所在位置。在目前的文獻中,學者們針對這類型的問題 (區間檢定),提供了不少方法,並且多數要求在執行方法前,對資料定義域均勻地切割,而切割的精細度決定了資料標定差異區間的準確度。然而,當差異區間越小,便須越精細的切割,否則容易檢測出過大的區間,並增加方法的錯誤拒絕率。此外,即便選擇一個相對更密集的切割,也得面臨計算時間上的需求,或是控制錯誤拒絕率對大樣本的要求。因此這篇論文我們針對區間檢定的前置步驟,分割,進行改良,以增強檢測的準確性。同時將其中一種現存的均值檢定法,從相同共變異數均值檢定推廣至相異共變異數均值檢定。最後將改良後的區間均值檢定法,應用於兩組資料 (氣象、車流量) 以展示改良前後與推廣前後的差異性。 | zh_TW |
dc.description.abstract | In two-sample tests for functional data, it is essential not only to determine overall differences but also to identify the specific locations of these differences. This presents what is known as an interval testing problem. Most existing methods require a pre-defined partition whose resolution may affect detection accuracy. However, a higher resolution necessitating a denser partition could lead to excessive computational time. Besides, although a higher resolution generally increases the detection precision, it also requires a larger sample size to control the same level of false discovery rates.
To address these issues, we have introduced a novel adjustment strategy that involves constructing a suitable partition as a preliminary step before implementing interval testing methods. This approach enhances the detection precision across various resolution scenarios. The concept is also extended to tests involving unequal sample covariances. Our simulation study indicates that the proposed approach yields higher statistical power in identifying significant intervals under small sample situations. We apply the approach to weather and traffic data, examining temperature differences at different locations and traffic flow differences on weekends, respectively. | en |
dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-08-05T16:24:32Z No. of bitstreams: 0 | en |
dc.description.provenance | Made available in DSpace on 2024-08-05T16:24:32Z (GMT). No. of bitstreams: 0 | en |
dc.description.tableofcontents | 摘要 i
Abstract iii Contents v List of Figures vii List of Tables ix Chapter 1 Introduction 1 1.1 Hypothesis testing in functional data . . . . . . . . . . . . . . . . . . 3 Chapter 2 Review of interval testing 7 2.1 Interval testing procedure (ITP) . . . . . . . . . . . . . . . . . . . . 7 2.2 Intervalwise testing (IWT) . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Partition closed testing (PCT) . . . . . . . . . . . . . . . . . . . . . 9 2.4 Thresholdwise testing (TWT) . . . . . . . . . . . . . . . . . . . . . 10 2.5 Remarks and potential issues . . . . . . . . . . . . . . . . . . . . . . 10 Chapter 3 The modified interval testing methods 13 3.1 The Improved Localization Partitioning . . . . . . . . . . . . . . . . 13 3.2 Adjustment for uncommon covariance and ITP extension . . . . . . . 17 3.3 Theoretical support of the modified interval testing methods . . . . . 18 Chapter 4 Simulation 21 4.1 Common covariance . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.1.1 Dense Significant Intervals (DSI) . . . . . . . . . . . . . . . . . . . 29 4.1.2 Effect of the adjacency parameter . . . . . . . . . . . . . . . . . . . 32 4.2 Uncommon covariance . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2.1 Simple covariance difference . . . . . . . . . . . . . . . . . . . . . 33 4.2.2 Tuning parameters . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.3 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Chapter 5 Applications 43 5.1 Canadian weather application . . . . . . . . . . . . . . . . . . . . . 43 5.2 Traffic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Chapter 6 Discussion 51 References 55 | - |
dc.language.iso | en | - |
dc.title | 精準化識別函數數據顯著差異區段之研究 | zh_TW |
dc.title | An improved testing procedure for localizing significant intervals for functional data | en |
dc.type | Thesis | - |
dc.date.schoolyear | 112-2 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 李百靈;蔡碧紋 | zh_TW |
dc.contributor.oralexamcommittee | Pai-Ling Li;Pi-Wen Tsai | en |
dc.subject.keyword | 雙樣本檢定,區間檢定,切割方法,均值檢定,拔靴法,偽發現率, | zh_TW |
dc.subject.keyword | Two sample testing,Interval testing,Partition,Mean test,Bootstrap,False discovery rate, | en |
dc.relation.page | 56 | - |
dc.identifier.doi | 10.6342/NTU202402123 | - |
dc.rights.note | 同意授權(限校園內公開) | - |
dc.date.accepted | 2024-07-29 | - |
dc.contributor.author-college | 理學院 | - |
dc.contributor.author-dept | 統計與數據科學研究所 | - |
dc.date.embargo-lift | 2029-07-26 | - |
顯示於系所單位: | 統計與數據科學研究所 |
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