A Bayesian approach to hybrid splines non-parametric regression

Journal of Statistical Computation and Simulation

Volumn 72, Issue 4, 2002, Pages 285-297

  Dias, Ronaldo ^a   Gamerman, Dani ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Hybrid splines non parametric regression; Reversible jump MCMC

Indexed keywords

EID: 0038826037     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949650212844     Document Type: Article

References (19)

1. k-smoothing splines. J. Statist. Plann. Inference, 49(3), 327-341.
2. Bates, D. and Wahba, G. (1982). Computational Methods for Generalized Cross Validation with Large Data Sets. Academic Press, London.
3. Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions. Numerische Mathematik, 31, 377-403.
4. de Boor, C. (1978). A Practical Guide to Splines. Springer Verlag, New York.
5. Denison, D. O. T., Mallick, B. K. and Smith, A. F. M. (1998). Automatic Bayesian curve fitting. Journal of the Royal Statistical Society B, 60, 363-377.
6. Dias, R. (1998). Density estimation via hybrid splines. Journal of Statistical Computation and Simulation, 60, 277-294.
7. Dias, R. (1999). Sequential adaptive non parametric regression via h-splines. Communications in Statistics: Computations and Simulations, 28, 501-515.
8. Donoho, D. L. and Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81(3), 425-455.
9. Gamerman, D. (1997). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman and Hall, London.
10. Green, P. J. (1995). Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732.
11. Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman and Hall.
12. Kimeldorf, G. S. and Wahba, G. (1970). A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. The Annals of Mathematical Statistics, 41, 495-502.
13. Luo, Z. and Wahba, G. (1997). Hybrid adaptive splines. Journal of the American Statistical Association, 92, 107-116.
14. Nychka, D. (1988). Bayesian confidence intervals for smoothing splines. J. Amer. Statist. Assoc., 83(404), 1134-1143.
15. Silverman, B. W. (1985), Some aspects of the spline smoothing approach to non-parametric regression curve fitting. Journal of the Royal Statistical Society, Series B, Methodological, 47, 1-21.
16. Silverman, B. W. and Green, P. J. (1994). Nonparametric Regression and Generalized Linear Models. Chapman and Hall, London.
17. Wahba, G. (1982). Constrained regularizarion for ill posed linear operator equations, with applications in meteorology and medicine. In: Gupta, S. S. and Berger, J. O. (Eds.), Statistical Decision Theory and Related Topics III, in two volumes, Vol. 2. Academic, NY, Lnd, pp. 383-418.
18. Wahba, G. (1983). Bayesian "confidence intervals" for the cross-validated smoothing spline. JRSS-B, Methodological, 45, 133-150.
19. Wegman, E. J. and Wright, I. W. (1983). Splines in statistics. Journal of the American Statistical Association, 78, 351-365.