5.10 文献笔记
5.10 文献笔记¶
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.