A class of template splines

Computational Statistics and Data Analysis

Volumn 50, Issue 12, 2006, Pages 3486-3499

  Sima, Diana M ^a   Van Huffel, Sabine ^a  

^a Katholieke Universiteit Leuven   (Belgium)

Author keywords

Nonparametric regression; Reproducing kernel Hilbert space; Splines

Indexed keywords

CONSTRAINT THEORY; LEAST SQUARES APPROXIMATIONS; NONLINEAR PROGRAMMING; PROBLEM SOLVING; REGRESSION ANALYSIS;

HILBERT SPACES; NONPARAMETRIC REGRESSION; REPRODUCING KERNEL HILBERT SPACE;

COMPUTATION THEORY;

EID: 33646678805     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2005.07.013     Document Type: Article

References (19)

1. Craven P., and Wahba G. Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math. 31 (1979) 377-403
2. de Boor C. A Practical Guide to Splines (1978), Springer, Berlin
3. Eilers P.H.C., and Marx B.D. Flexible smoothing with B-splines and penalties. Statist. Sci. 11 2 (1997) 89-121
4. Eubank R. Nonparametric Regression and Spline Smoothing (1999), Marcel Dekker, New York
5. Friedman, J.H., 1991. Multivariate adaptive regression splines (with discussion). Ann Staist. 19 (1).
6. Golub G.H., and Van Loan C.F. Matrix Computations. third ed (1996), Johns Hopkins University Press, Baltimore, Maryland
7. Golub G.H., and von Matt U. Generalized cross-validation for large scale problems. In: Van Huffel S. (Ed). Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling (1997), SIAM 139-148
8. Golub G.H., Heath M., and Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21 (1979) 215-223
9. Green P.J., and Silverman B.W. Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach (1994), Chapman & Hall, London
10. Hall P., and Opsomer J. Theory for penalised spline regression. Biometrika 92 (2005) 105-118
11. Hansen P.C. Rank-Deficient and Discrete Ill-Posed Problems. Numerical Aspects of Linear Inversion (1997), SIAM, Philadelphia
12. Härdle W. Applied Nonparametric Regression. Econometric Society Monographs (1990), Cambridge University Press, Cambridge
13. Kuijt F., and van Damme R. A linear approach to shape preserving spline approximation. Adv. Comput. Math. 14 (2001) 25-48
14. Lee T.C.M. Smoothing parameter selection for smoothing splines. a simulation study. Comput. Statist. Data Anal. 42 1-2 (2003) 139-148
15. Mammen E., Marron J., Turlach B., and Wand M. A general projection framework for constrained smoothing. Statist. Sci. 16 3 (2001) 232-248
16. Ruppert D. Selecting the number of knots for penalized splines. J. Comput. Graphical Statist. 11 (2002) 735-757
17. Ruppert, D., Carroll, R., 1996. A simple roughness penalty approach to regression spline estimation. Technical Report 1167, School of OR&IE, Cornell University.
18. Wahba G. Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics 59 (1990), SIAM, Philadelphia, PA
19. Wahba, G., August 2003. An introduction to reproducing kernel Hilbert spaces and why are they so useful. In: Proceedings of the 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam.