Spline smoothing over difficult regions

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 64, Issue 2, 2002, Pages 307-319

  Ramsay, Tim ^a,b  

^a M Ctr for Pop Hlth Risk Assess   (Canada)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Bivariate spline; Finite element; Penalized regression; Smoothing; Spatial smoothing; Thin plate spline

Indexed keywords

EID: 0036013002     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00339     Document Type: Article

References (19)

1. Braess, D. (1997) Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge: Cambridge University Press.
2. Brenner, S.C. and Scott, L.R. (1994) The Mathematical Theory of Finite Elements. New York: Springer.
3. Carey, G. and Oden, J. (1983) Finite Elements: a Second Course. Englewood Cliffs: Prentice Hall.
4. Cowling, A., Chambers, R., Lindsay, R. and Parameswaran, B. (1996) Applications of spatial smoothing to survey data. Surv. Methodol., 22, 175-183.
5. Dierkcx, P. (1993) Curve and Surface Fitting with Splines. Oxford: Oxford University Press.
6. Duchon, J. (1976) Interpolation des fonctions de deux variables suivant le principe de la flexion des placques minces. Rev. Fr. Autom. Inform. Rech. Oper. Anal. Numer., 10, 5-12.
7. Dyn, N. and Levin, D. (1982) Construction of surface spline interpolants of scattered data over finite domains. Rev. Fr. Autom. Inform. Rech. Oper. Anal. Numer., 16, 201-209.
8. Folland, G.B. (1995) Introduction to Partial Differential Equations. Princeton: Princeton University Press.
9. Hanselman, D. and Littlefield, B. (1998) Mastering MATLAB 5: a Comprehensive Tutorial and Reference. Upper Saddle River: Prentice Hall.
10. Heckman, N. and Ramsay, J.O. (2000) Penalized regression with model-based penalties. Can. J. Statist., 28, 241-258.
11. Hinkley, D.V. (1988) Bootstrap methods. J. R. Statist. Soc. B, 50, 321-337.
12. Horgan, G.W. (1999) Using wavelets for data smoothing: a simulation study. J. Appl. Statist., 26, 923-932.
13. Meiring, W., Guttorp, P. and Sampson, P. (1997) Computational issues in fitting spatial deformation models for heterogeneous spatial correlation. In Computing Science and Statistics; Mining and Modeling Massive Data Sets in Science, Engineering, and Business with a Subtheme in Environmental Science: Proc. 29th Symp. Interface, pp. 409-417. Fairfax Station: Interface Foundation of North America.
14. O'Connell, M.A. and Wolfinger, R.D. (1997) Spatial regression models, response surfaces, and process optimization. J. Comput. Graph. Statist., 6, 224-241.
15. Ramsay, J.O. (2000) Differential equation models for statistical functions. Can. J. Statist., 28, 224-240.
16. Sibson, R. and Stone, G. (1991) Computation of thinplate splines. SIAM J. Statist. Scient. Comput., 12, 1304-1313.
17. Stone, G. (1988) Bivariate splines. PhD Thesis. University of Bath, Bath.
18. Wahba, G. (1990) Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.
19. Wand, M.P. and Jones, M.C. (1995) Kernel Smoothing. London: Chapman and Hall.