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題名 曲線相似性之檢定
A test for curve similarity作者 程毓婷
Cheng, Yu Ting貢獻者 黃子銘
Huang, Tzee Ming
程毓婷
Cheng, Yu Ting關鍵詞 時間對齊函數
共同外形
warping function
common shape
B-spline日期 2010 上傳時間 5-Sep-2013 15:13:19 (UTC+8) 摘要 這篇論文提出了比較兩組資料曲線在對齊後是否有相似外形的分析方法。在 functional data analysis 中，可能會有多條曲線具有相同外形但是時間轉換卻不一樣的情形。這篇論文檢定了兩組資料曲線在對齊後是否有相似外形，論文中並提出一個檢定統計量，再藉由模擬得到檢定的 p-value 和檢定力。
This thesis proposed an analysis comparing whether the shape function for two groups of curves are similar after alignment. In functional data analysis, it is common to have curves of the same pattern but with variation in time. The common pattern can be characterized by a shape function. The problem considered in this thesis is to test whether the shape functions for two groups of curves are essentially the same. A test statistic is proposed and the p-value is obtained via simulation. Simulation results indicate that the test performs well.參考文獻 [1] Jeremie Bigot. Landmark-based registration of curves via the continuous wavelet transform. Journal of Computational and Graphical Statistics, 15(3):542-564, 2006.[2] Theo Gasser and Alois Kneip. Searching for structure in curve samples. Journal of the American Statistical Association, 90:1179-1188, 1995.[3] Daniel Gervini and Theo Gasser. Self-modelling warping functions. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 66(4):959-971, 2004.[4] C. A. Glasbey and K. V. Mardia. A review of image-warping methods. Journal of Applied Statistics, 25:155-171, 1998.[5] A. Kneip, X. Li, K. B. MacGibbon, and J. O. Ramsay. Curve registration by local regression. The Canadian Journal of Statistics / La Revue Canadienne de Statistique, 28(1):19-29, 2000.[6] Alois Kneip and Theo Gasser. Statistical tools to analyze data representing a sample of curves. The Annals of Statistics, 20:1266-1305, 1992.[7] Xueli Liu and Hans-Georg Muller. Functional convex averaging and synchronization for time-warped random curves. Journal of the American Statistical Association, 99(467):687-699, 2004.[8] Yolanda Munoz Maldonado, Yolanda Munoz Maldonado, Joan G. Staniswalis, Louis N. Irwin, and Donna Byers. A similarity analysis of curves. The Canadian Journal of Statistics / La Revue Canadienne de Statistique, 30(3):373-381, 2002.[9] J. O. Ramsay and Xiaochun Li. Curve registration. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 60:351-363, 1998.[10] J. O. Ramsay and B. W. Silverman. Functional Data Analysis. Springer-Verlag Inc, 1997.[11] Birgitte B. Ronn, Birgitte B. Ronn, and Birgitte B. Roenn. Nonparametric maximum likelihood estimation for shifted curves. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 63(2):243-259, 2001.[12] H. Sakoe and S. Chiba. Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. on Acoust., Speech, and Signal Processing, ASSP-26(1):43-49, 1978.[13] Rong Tang and Hans-Georg Muller. Pairwise curve synchronization for functional data. Biometrika, 95(4):875-889, 2008.[14] Donatello Telesca and Lurdes Y. T. Inoue. Bayesian Hierarchical Curve Registration. Journal of the American Statistical Association, 103(481):328-339, 2008.[15] Grace Wahba. Spline Models for Observational Data. SIAM [Society for Industrial and Applied Mathematics], 1990.[16] Kongming Wang and Theo Gasser. Alignment of curves by dynamic time warping. The Annals of Statistics, 25(3):1251-1276, 1997. 描述 碩士
國立政治大學
統計研究所
98354017
99資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098354017 資料類型 thesis dc.contributor.advisor 黃子銘 zh_TW dc.contributor.advisor Huang, Tzee Ming en_US dc.contributor.author (Authors) 程毓婷 zh_TW dc.contributor.author (Authors) Cheng, Yu Ting en_US dc.creator (作者) 程毓婷 zh_TW dc.creator (作者) Cheng, Yu Ting en_US dc.date (日期) 2010 en_US dc.date.accessioned 5-Sep-2013 15:13:19 (UTC+8) - dc.date.available 5-Sep-2013 15:13:19 (UTC+8) - dc.date.issued (上傳時間) 5-Sep-2013 15:13:19 (UTC+8) - dc.identifier (Other Identifiers) G0098354017 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60444 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 98354017 zh_TW dc.description (描述) 99 zh_TW dc.description.abstract (摘要) 這篇論文提出了比較兩組資料曲線在對齊後是否有相似外形的分析方法。在 functional data analysis 中，可能會有多條曲線具有相同外形但是時間轉換卻不一樣的情形。這篇論文檢定了兩組資料曲線在對齊後是否有相似外形，論文中並提出一個檢定統計量，再藉由模擬得到檢定的 p-value 和檢定力。 zh_TW dc.description.abstract (摘要) This thesis proposed an analysis comparing whether the shape function for two groups of curves are similar after alignment. In functional data analysis, it is common to have curves of the same pattern but with variation in time. The common pattern can be characterized by a shape function. The problem considered in this thesis is to test whether the shape functions for two groups of curves are essentially the same. A test statistic is proposed and the p-value is obtained via simulation. Simulation results indicate that the test performs well. en_US dc.description.tableofcontents 1 緒論 42 文獻回顧 63 研究方法 84 模擬過程 125 結果與討論 25 zh_TW dc.format.extent 844222 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0098354017 en_US dc.subject (關鍵詞) 時間對齊函數 zh_TW dc.subject (關鍵詞) 共同外形 zh_TW dc.subject (關鍵詞) warping function en_US dc.subject (關鍵詞) common shape en_US dc.subject (關鍵詞) B-spline en_US dc.title (題名) 曲線相似性之檢定 zh_TW dc.title (題名) A test for curve similarity en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [1] Jeremie Bigot. Landmark-based registration of curves via the continuous wavelet transform. Journal of Computational and Graphical Statistics, 15(3):542-564, 2006.[2] Theo Gasser and Alois Kneip. Searching for structure in curve samples. Journal of the American Statistical Association, 90:1179-1188, 1995.[3] Daniel Gervini and Theo Gasser. Self-modelling warping functions. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 66(4):959-971, 2004.[4] C. A. Glasbey and K. V. Mardia. A review of image-warping methods. Journal of Applied Statistics, 25:155-171, 1998.[5] A. Kneip, X. Li, K. B. MacGibbon, and J. O. Ramsay. Curve registration by local regression. The Canadian Journal of Statistics / La Revue Canadienne de Statistique, 28(1):19-29, 2000.[6] Alois Kneip and Theo Gasser. Statistical tools to analyze data representing a sample of curves. The Annals of Statistics, 20:1266-1305, 1992.[7] Xueli Liu and Hans-Georg Muller. Functional convex averaging and synchronization for time-warped random curves. Journal of the American Statistical Association, 99(467):687-699, 2004.[8] Yolanda Munoz Maldonado, Yolanda Munoz Maldonado, Joan G. Staniswalis, Louis N. Irwin, and Donna Byers. A similarity analysis of curves. The Canadian Journal of Statistics / La Revue Canadienne de Statistique, 30(3):373-381, 2002.[9] J. O. Ramsay and Xiaochun Li. Curve registration. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 60:351-363, 1998.[10] J. O. Ramsay and B. W. Silverman. Functional Data Analysis. Springer-Verlag Inc, 1997.[11] Birgitte B. Ronn, Birgitte B. Ronn, and Birgitte B. Roenn. Nonparametric maximum likelihood estimation for shifted curves. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 63(2):243-259, 2001.[12] H. Sakoe and S. Chiba. Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. on Acoust., Speech, and Signal Processing, ASSP-26(1):43-49, 1978.[13] Rong Tang and Hans-Georg Muller. Pairwise curve synchronization for functional data. Biometrika, 95(4):875-889, 2008.[14] Donatello Telesca and Lurdes Y. T. Inoue. Bayesian Hierarchical Curve Registration. Journal of the American Statistical Association, 103(481):328-339, 2008.[15] Grace Wahba. Spline Models for Observational Data. SIAM [Society for Industrial and Applied Mathematics], 1990.[16] Kongming Wang and Theo Gasser. Alignment of curves by dynamic time warping. The Annals of Statistics, 25(3):1251-1276, 1997. zh_TW
