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5.10 文献笔记

原文 The Elements of Statistical Learning
翻译 szcf-weiya
时间 2017-09-10

样条和B样条在de Boor (1978)1中有详细讨论.Green and Silverman (1994)2和Wahba (1990)给出了光滑样条以及thin-plate样条的;后者也产生核Hilbert空间.关于采用RKHS方法的非参回归技巧的联系可以参见Girosi et al. (1995)3 和Evgeniou et al. (2000)4.如5.2.3节所示,对函数数据建模,在Ramsay and Silverman (1997)5中有详细介绍.

Daubechies (1992)6是一个经典的、小波的数学处理.其它有用的资源有Chui (1992)7和Wickerhauser (1994)8.Donoho and Johnstone (1994)9从统计估计的框架下发展了SURE收缩和选择的技巧;也可以参见Vidakovic (1999)10.Bruce and Gao (1996)11是很有用的应用介绍,它也描述了S-PLUS中的小波软件.


  1. de Boor, C. (1978). A Practical Guide to Splines, Springer, New York. 

  2. Green, P. and Silverman, B. (1994). Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, London. 

  3. Girosi, F., Jones, M. and Poggio, T. (1995). Regularization theory and neural network architectures, Neural Computation 7: 219–269. 

  4. Evgeniou, T., Pontil, M. and Poggio, T. (2000). Regularization networks and support vector machines, Advances in Computational Mathematics 13(1): 1–50. 

  5. Ramsay, J. and Silverman, B. (1997). Functional Data Analysis, Springer, New York. 

  6. Daubechies, I. (1992). Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA. 

  7. Chui, C. (1992). An Introduction to Wavelets, Academic Press, London. 

  8. Wickerhauser, M. (1994). Adapted Wavelet Analysis from Theory to Software, A.K. Peters Ltd, Natick, MA. 

  9. Donoho, D. and Johnstone, I. (1994). Ideal spatial adaptation by wavelet shrinkage, Biometrika 81: 425–455. 

  10. Vidakovic, B. (1999). Statistical Modeling by Wavelets, Wiley, New York. 

  11. Bruce, A. and Gao, H. (1996). Applied Wavelet Analysis with S-PLUS, Springer, New York. 

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