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題名 小波理論在平滑函數估計上之探討
作者 蔡淑貞
Tsai, Shu-Jane
貢獻者 張健邦
Jang, Jiahn-Bang
蔡淑貞
Tsai, Shu-Jane
日期 1996
上傳時間 10-五月-2016 18:56:18 (UTC+8)
摘要 近幾十年來，有許多學者都致力於平滑函數估計的研究並發展出多種的平滑函數估計方法。縱觀過去學者所提出的平滑函數估計法，皆有一共同特徵：即是設法消除函數觀測值所受之干擾，藉由干擾的降低以尋求未知平滑函數之估計值。
在小波理論和應用的研究中，都顯示出小波轉換法具有優越地降低干擾訊息的特性，應用於降低未知平滑函數觀測值之干擾，並以其估計未知函數。最後並在模擬試驗中和其他平滑函數估計法相比較，以探討其優劣性。
參考文獻 一、中文部份
[1] 鄭錦聰， MATLAB 入門引導(民國84 年) ，全華科技圖書公司。

二、英文部分
[2] Antoniadis, A., 1994, Smoothing Noise Data with Coiflets, Statistica Sinica, Vol. 4, No.2, 651-678.
[3] Antoniadis, A. and Lavergne, c., 1995, Variance Function Estimation in Regression by Wavelet Methods, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), Springer-Verlag Press,
New York, 31-42 .
[4] Abramovich, F. and Benjamini, Y., 1995, Thresholding of Wavelet Coefficients as Multiple Hypothesis Testing Procedure, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), SpringerVerlag
Press, New York, 5-14.
[5] Abramovich, F. and Benjamini, Y., 1995, Thresholding of Wavelet Coefficients as Multiple Hypothesis Testing Procedure, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), SpringerVerlag Press, New York, 5-14
[6] Battle, G. and Federbush, P., Ondelettes and Phase Cell Cluster Expansions: A Vindication, Comm. Math. Phys. Vol. 109,417-419.
[7] Benjamini, Y. and Hochberg, Y., 1995, Controlling the False Discovery Rate : A Practical and Powerful Approach to Multiple Testing, Journal Royal Statistical Society B, 57, 289-300.
[8] Breiman L. and Peters, S., 1992, Comparing Automatic Smoothers, Internet. Statist. Rev., 60,271-290.
[9] Buckheit, 1. B. and Donoho, D. L., 1995, Wavelab and Reproducible Research, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), Springer-Verlag Press, New York, 55-81.
[10] Chui, c. K., 1992, An Introduction to Wavelets, Academic Press, New York.
[11] Cleveland, W. S., 1979, Robust Locally Weighted Regression and Smoothing Scatterplots, Journal of the American Statistical Association, 74, 829-836.
[12] Daubechies, I., 1988, Orthonormal Bases of Compactly Supported Wavelets, Comm. Pure and Appl. Math., 41,909-996.
[13] Daubechies, I., 1990, OrthonOImal Bases of Compactly Supported Wavelets 2, Variation on a Theme. Preprint, submitted to SlAM Journal Math. Anal.
[14] Daubechies, I., 1992, Ten Lecture on Wavelet, SIAM, CBMS Series, April.
[15] Daubechies, 1., Grossmann, A. and Meyer, Y., 1986, Painless Nonorthogonal Expansions, 1. Math. Phys., 27, 1271-1283.
[16] Donoho, D. L. and Johnstone, 1. M., 1994(a), Adapting to Unknown Smoothness via Wavelet Sluinkage, 1. Amer. Stat. Stat. Assoc. ( to appear ). ftp://playfair.stanford.eduJpub/donoho/ausws.ps .Z
[17] Donoho, D. L. and Johnstone, 1. M., 1994(b), Ideal Spatial Adaptation by Wavelet Shrinkage, Biometrika, 81, 425-455.
ftp://playfair.stanford.eduJpub/donoho/isaws. ps.Z
[18] Dooijes, E. H., 1993, Conjugate Quadrature Filters for Multiresolution Analysis and Synthesis, In Wavelets : An Elementary Treatment of Theory and Applications( Koomwinder, T. H. eds. ), World Scientific Press, USA, 129-138.
[19] Gabor, D., 1946, Theory of Communication, Journal of the lEE., Vol.93,429-457.
[20] Grossmann, A, and Morlet, 1., 1984, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SlAM 1. Math., Vol. 15, No. 14,723-736.
[21] Hastie, T. 1. and Tibshirani, R. 1., 1990, Generalized Additive Models, Chapman and Hall, London.
[22] Kay,1.; 1994, Wavelets, Advance in Applied Statistics, 209-224
[23] Mallat, S. G., 1989(a), A Theory for Multiresolution Signal Decomposition: The Wavelet Representation, IEEE Trans. Pattern Analysis and Machine intelligence., Vol. 11, No.7, July.
[24] Mallat, S. G., 1989(b),Multiresolution Approximation and Wavelet OrthonoIIDal Bases of L2(R), Transactions of the American Mathmatical SOCiety, 315, 69-87.
[25] MATLAB User`s Guide, 1992, Ver. 4, The Math Works Inc ..
[26] MATLAB Reference Guide, 1992, Ver. 4, The Math Works Inc ..
[27] Meyer, Y., 1985, Principe D`incertitude, Bases Hilbertiennes et Algebres D`operateurs, Bourbaki Seminar, No. 662.
[28] Morlet, 1. and Grossmann, A., 1984, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SlAM J. Math., Vol. 15, 723-736.
[29] Nason, G. P., 1994, Wavelet Regression by Cross-Validation, Technical Report 447, Department of Statistics, Stanford University, Stanford.
[30] Nason, G. P., 1995, Choice of the Threshold Parameter in Wavelet Function Estimation, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), Springer-Verlag Press, New York, 261-280.
[31] Nussbaum, M., 1985, Spline Smoothing in Regression Models and Asymptotic Efficiency in 4, Ann. Statist, 13, 984-997.
[32] Press, W. H., 1991, Wavelet Transform, Technique Report by Numerical Recipes Software.
[33] Rioul, O. and Vetterli, M., 1991, Wavelets and Signal Processing, IEEE SP Magazine, 14-38.
[34] S-PLUS Guide to Statistical and Mathematical Analysis, 1993, Verso 3.2, StatSci, a division of MathSoft, Inc ..
[35] Silverman, B. W., 1986, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
[36] Stone, C. 1., 1982, Optimal Global Rates of Convergence for nonparametric Regression, Ann. Statist, 10, 1040-1053 .
[37] Strang, G., 1989, Wavelets and Dilation Equations, SIAM Review, Vol. 31, 614-627.
[38] Venables, W. N. and Ripley, B. D., 1994, Modern Applied Statistics with S-Plus, Springer-Verlag Press, New York.
[39] Vidakovic, B., 1994, Nonlinear Wavelet Shrinkage with Bayes Rules and Bayes Factors, (submitted for publication).
[40] Wang, Y., 1994, Function Estimation via Wavelets for Data with Long-Range Dependence, Technical Report, University of Missouri, Columbia.
[41.] Zhang, Q., 1995, Wavelets and Regression Analysis, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), Springer-Verlag Press, New York, 397-407.
描述 碩士
國立政治大學
統計學系
資料來源 http://thesis.lib.nccu.edu.tw/record/#G91NCCV0952012
資料類型 thesis
dc.contributor.advisor 張健邦zh_TW
dc.contributor.advisor Jang, Jiahn-Bangen_US
dc.contributor.author (作者) 蔡淑貞zh_TW
dc.contributor.author (作者) Tsai, Shu-Janeen_US
dc.creator (作者) 蔡淑貞zh_TW
dc.creator (作者) Tsai, Shu-Janeen_US
dc.date (日期) 1996en_US
dc.date.accessioned 10-五月-2016 18:56:18 (UTC+8)-
dc.date.available 10-五月-2016 18:56:18 (UTC+8)-
dc.date.issued (上傳時間) 10-五月-2016 18:56:18 (UTC+8)-
dc.identifier (其他 識別碼) G91NCCV0952012en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/96302-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description.abstract (摘要) 近幾十年來，有許多學者都致力於平滑函數估計的研究並發展出多種的平滑函數估計方法。縱觀過去學者所提出的平滑函數估計法，皆有一共同特徵：即是設法消除函數觀測值所受之干擾，藉由干擾的降低以尋求未知平滑函數之估計值。
在小波理論和應用的研究中，都顯示出小波轉換法具有優越地降低干擾訊息的特性，應用於降低未知平滑函數觀測值之干擾，並以其估計未知函數。最後並在模擬試驗中和其他平滑函數估計法相比較，以探討其優劣性。		zh_TW
dc.description.tableofcontents 第一章 緒論
1.1 研究動機與目的..........1
1.2 研究步驟..........2
1.3 章節架構..........3
第二章 小波理論
2.1 小波理論發展簡介..........5
2.2 數學符號之定義與說明..........6
2.3富立葉轉換法與視窗富立葉轉換法..........8
2.4小波轉換..........10
2.4.1 連續型小波轉換..........11
2.4.2 間斷型小波轉換..........12
2.5多重解析分析..........13
2.5.1 多重解析分析的基本概念..........13
2.5.2 多重解析分析之分解與重建..........15
第三章 小波平滑函數估計法
3.1 專有名詞介紹..........20
3.2 無母數函數估計-小波法..........22
3.3 小波門檻..........28
第四章 模擬與實證分析
4.1 模擬資料分析與比較..........32
4.1.1 模擬資料之小波函數估計..........32
4.1.2 平滑函數估計法之比較..........37
4.2 實證資料分析──以臺灣股票總加權指數為例..........42
第五章 結論與建議
5.1 結論..........45
5.2 研究限制與建議..........45
參考文獻..........49
附錄A..........54
附錄B..........56		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G91NCCV0952012en_US
dc.title (題名) 小波理論在平滑函數估計上之探討zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 一、中文部份
[1] 鄭錦聰， MATLAB 入門引導(民國84 年) ，全華科技圖書公司。

二、英文部分
[2] Antoniadis, A., 1994, Smoothing Noise Data with Coiflets, Statistica Sinica, Vol. 4, No.2, 651-678.
[3] Antoniadis, A. and Lavergne, c., 1995, Variance Function Estimation in Regression by Wavelet Methods, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), Springer-Verlag Press,
New York, 31-42 .
[4] Abramovich, F. and Benjamini, Y., 1995, Thresholding of Wavelet Coefficients as Multiple Hypothesis Testing Procedure, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), SpringerVerlag
Press, New York, 5-14.
[5] Abramovich, F. and Benjamini, Y., 1995, Thresholding of Wavelet Coefficients as Multiple Hypothesis Testing Procedure, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), SpringerVerlag Press, New York, 5-14
[6] Battle, G. and Federbush, P., Ondelettes and Phase Cell Cluster Expansions: A Vindication, Comm. Math. Phys. Vol. 109,417-419.
[7] Benjamini, Y. and Hochberg, Y., 1995, Controlling the False Discovery Rate : A Practical and Powerful Approach to Multiple Testing, Journal Royal Statistical Society B, 57, 289-300.
[8] Breiman L. and Peters, S., 1992, Comparing Automatic Smoothers, Internet. Statist. Rev., 60,271-290.
[9] Buckheit, 1. B. and Donoho, D. L., 1995, Wavelab and Reproducible Research, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), Springer-Verlag Press, New York, 55-81.
[10] Chui, c. K., 1992, An Introduction to Wavelets, Academic Press, New York.
[11] Cleveland, W. S., 1979, Robust Locally Weighted Regression and Smoothing Scatterplots, Journal of the American Statistical Association, 74, 829-836.
[12] Daubechies, I., 1988, Orthonormal Bases of Compactly Supported Wavelets, Comm. Pure and Appl. Math., 41,909-996.
[13] Daubechies, I., 1990, OrthonOImal Bases of Compactly Supported Wavelets 2, Variation on a Theme. Preprint, submitted to SlAM Journal Math. Anal.
[14] Daubechies, I., 1992, Ten Lecture on Wavelet, SIAM, CBMS Series, April.
[15] Daubechies, 1., Grossmann, A. and Meyer, Y., 1986, Painless Nonorthogonal Expansions, 1. Math. Phys., 27, 1271-1283.
[16] Donoho, D. L. and Johnstone, 1. M., 1994(a), Adapting to Unknown Smoothness via Wavelet Sluinkage, 1. Amer. Stat. Stat. Assoc. ( to appear ). ftp://playfair.stanford.eduJpub/donoho/ausws.ps .Z
[17] Donoho, D. L. and Johnstone, 1. M., 1994(b), Ideal Spatial Adaptation by Wavelet Shrinkage, Biometrika, 81, 425-455.
ftp://playfair.stanford.eduJpub/donoho/isaws. ps.Z
[18] Dooijes, E. H., 1993, Conjugate Quadrature Filters for Multiresolution Analysis and Synthesis, In Wavelets : An Elementary Treatment of Theory and Applications( Koomwinder, T. H. eds. ), World Scientific Press, USA, 129-138.
[19] Gabor, D., 1946, Theory of Communication, Journal of the lEE., Vol.93,429-457.
[20] Grossmann, A, and Morlet, 1., 1984, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SlAM 1. Math., Vol. 15, No. 14,723-736.
[21] Hastie, T. 1. and Tibshirani, R. 1., 1990, Generalized Additive Models, Chapman and Hall, London.
[22] Kay,1.; 1994, Wavelets, Advance in Applied Statistics, 209-224
[23] Mallat, S. G., 1989(a), A Theory for Multiresolution Signal Decomposition: The Wavelet Representation, IEEE Trans. Pattern Analysis and Machine intelligence., Vol. 11, No.7, July.
[24] Mallat, S. G., 1989(b),Multiresolution Approximation and Wavelet OrthonoIIDal Bases of L2(R), Transactions of the American Mathmatical SOCiety, 315, 69-87.
[25] MATLAB User`s Guide, 1992, Ver. 4, The Math Works Inc ..
[26] MATLAB Reference Guide, 1992, Ver. 4, The Math Works Inc ..
[27] Meyer, Y., 1985, Principe D`incertitude, Bases Hilbertiennes et Algebres D`operateurs, Bourbaki Seminar, No. 662.
[28] Morlet, 1. and Grossmann, A., 1984, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SlAM J. Math., Vol. 15, 723-736.
[29] Nason, G. P., 1994, Wavelet Regression by Cross-Validation, Technical Report 447, Department of Statistics, Stanford University, Stanford.
[30] Nason, G. P., 1995, Choice of the Threshold Parameter in Wavelet Function Estimation, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), Springer-Verlag Press, New York, 261-280.
[31] Nussbaum, M., 1985, Spline Smoothing in Regression Models and Asymptotic Efficiency in 4, Ann. Statist, 13, 984-997.
[32] Press, W. H., 1991, Wavelet Transform, Technique Report by Numerical Recipes Software.
[33] Rioul, O. and Vetterli, M., 1991, Wavelets and Signal Processing, IEEE SP Magazine, 14-38.
[34] S-PLUS Guide to Statistical and Mathematical Analysis, 1993, Verso 3.2, StatSci, a division of MathSoft, Inc ..
[35] Silverman, B. W., 1986, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
[36] Stone, C. 1., 1982, Optimal Global Rates of Convergence for nonparametric Regression, Ann. Statist, 10, 1040-1053 .
[37] Strang, G., 1989, Wavelets and Dilation Equations, SIAM Review, Vol. 31, 614-627.
[38] Venables, W. N. and Ripley, B. D., 1994, Modern Applied Statistics with S-Plus, Springer-Verlag Press, New York.
[39] Vidakovic, B., 1994, Nonlinear Wavelet Shrinkage with Bayes Rules and Bayes Factors, (submitted for publication).
[40] Wang, Y., 1994, Function Estimation via Wavelets for Data with Long-Range Dependence, Technical Report, University of Missouri, Columbia.
[41.] Zhang, Q., 1995, Wavelets and Regression Analysis, In Wavelets and Statistics ( Antoniadis, A. and Oppenheim, G. eds. ), Springer-Verlag Press, New York, 397-407.		zh_TW