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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 Mingen_US
dc.contributor.author (Authors) 程毓婷zh_TW
dc.contributor.author (Authors) Cheng, Yu Tingen_US
dc.creator (作者) 程毓婷zh_TW
dc.creator (作者) Cheng, Yu Tingen_US
dc.date (日期) 2010en_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) G0098354017en_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) 98354017zh_TW
dc.description (描述) 99zh_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 4
2 文獻回顧 6
3 研究方法 8
4 模擬過程 12
5 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/#G0098354017en_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 functionen_US
dc.subject (關鍵詞) common shapeen_US
dc.subject (關鍵詞) B-splineen_US
dc.title (題名) 曲線相似性之檢定zh_TW
dc.title (題名) A test for curve similarityen_US
dc.type (資料類型) thesisen
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