State space representation for smoothing spline ANOVA models

Journal of Computational and Graphical Statistics

Volumn 15, Issue 4, 2006, Pages 830-847

  Qin, Li ^a   Guo, Wensheng ^b  

^a Fred Hutchinson Cancer Research Center   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

High dimensional smoothing; Kalman filter; Multivariate spline; Non parametric regression; State space model; Tensor product; Time series

Indexed keywords

EID: 33846142153     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186006X157568     Document Type: Article

References (24)

1. Anderson, B. O., and Moore, J. B. (1979), Optimal Filtering, Englewood Cliffs: Prentice-Hall.
2. Ansley, C. F., and Kohn, R. (1985), "Estimation, Filtering and Smoothing in State Space Models with Incompletely Specified Initial Conditions," The Annals of Statistics, 13, 1286-1316.
3. Aronszajn, N. (1950), "Theory of Reproducing Kernels," Transactions of the American Mathematical Society, 68, 337-404.
4. Dahlhaus, R. (1997), "Fitting Time Series Models to Nonstationary Processes," The Annals of Statistics, 25, 1-37.
5. De Jong, P. (1988), "A Cross-Validation Filter for Time Series Models," Biometrika, 75, 594-600.
6. Durbin, J., and Koopman, S.J. (2001), Time Series Analysis by State Space Methods, New York: Oxford University Press.
7. Green, P. J., and Silverman, B. W. (1994), Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, London: Chapman and Hall.
8. Gu, C. (1989), "RKpack and its Application: Fitting Smoothing Spline Models," in Proceedings of the Statistical Computing Section, Fairfax, VA: American Statistical Association, pp. 42-51.
9. _ (1993), "Interaction Splines with Regular Data: Automatically Smoothing Digital Images," SIAM Journal of Scientific Computing, 14, 218-230.
10. _ (2002), Smoothing Spline ANOVA Models, New York: Springer-Verlag.
11. Gu, C., and Wahba, G. (1993a), "Semiparametric Analysis of Variance with Tensor Product thin Plate Splines," Journal of the Royal Statistical Society, Series B, 55, 353-368.
12. _ (1993b), "Smoothing Spline ANOVA With Components-Wise Bayesian Confidence Intervals," Journal of Computational and Graphical Statistics, 1, 97-117.
13. Guo, W., Dai, M., Omhao, H., and von Sachs, R. (2003), "Smoothing Spline ANOVA for Time-Dependent Spectral Analysis," Journal of the American Statistical Association, 98, 643-652.
14. Kim, Y. J., and Gu, C. (2004), "Smoothing Spline Gaussian Regression: More Scalable Computation via Efficient Approximation," Journal of the Royal Statistical Society, Series B, 66, 337-356.
15. Kohn, R., and Ansley, C. F. (1989), "A Fast Algorithm for Signal Extraction, Influence and Cross Validation in State Space Models," Biometrika, 76, 65-79.
16. Koopman, S. J. (1997), "Exact Initial Kalman Filtering and Smoothing for Nonstationary Time Series Models," Journal of the American Statistical Association, 92, 1630-1638.
17. Koopman, S. J., and Durbin, J. (2000), "Fast Filtering and Smoothing for Multivariate State Space Models," Journal of Time Series Analysis, 21, 281-296.
18. Priestley, M. B. (1981), Spectral Analysis and Time Series, London: Academic Press.
19. _ (1988), Non-Linear and Non-Stationary Time Series, London: Academic Press.
20. Wahba, G. (1978), "Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Error in Regression," Journal of the Royal Statistical Society, Series B, 40, 364-372.
21. _ (1983), "Bayesian Confidence Intervals for the Cross-Validated Smoothing Spline," Journal of the Royal Statistical Society, Series B, 45, 133-150.
22. _ (1985), "A Comparison of GCV and GML for Choosing the Smoothing Parameters in the Generalized Spline Smoothing Problem," The Annals of Statistics, 13, 1378-1402.
23. _ (1990), Spline Models for Observational Data, Volume 59 of CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia: SIAM.
24. Wecker, W. E., and Ansley, C. F. (1983), "The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing," Journal of the American Statistical Association, 78, 81-89.