Coverage Properties of Confidence Intervals for Generalized Additive Model Components

Scandinavian Journal of Statistics

Volumn 39, Issue 1, 2012, Pages 53-74

  Marra, Giampiero ^a   Wood, Simon N ^b  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

Bayesian confidence interval; Generalized additive model; Penalized regression spline

Indexed keywords

EID: 84857058351     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2011.00760.x     Document Type: Article

References (26)

1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In International symposium on information theory (eds B. Petran and F. Csaaki ), 267-281, Budapest.
2. Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions. Numer. Math. 31, 377-403.
3. Fahrmeir, L., Kneib, T. and Lang, S. (2004). Penalized structured additive regression for space-time data: a Bayesian perspective. Statist. Sinica 14, 731-761.
4. Fahrmeir, L. and Lang, S. (2001). Bayesian inference for generalized additive mixed models based on Markov random field priors. J. Roy. Statist. Soc. C App. 50, 201-220.
5. Gentle, J. E. (2003). Random number generation and Monte Carlo methods. Springer-Verlag, London.
6. Gu, C. (1992). Penalized likelihood regression - a Bayesian analysis. Statist. Sinica 2, 255-264.
7. Gu, C. (2002). Smoothing spline ANOVA models. Springer-Verlag, London.
8. Gu, C. and Wahba, G. (1993). Smoothing spline ANOVA with component-wise Bayesian confidence intervals. J. Comp. Graph. Stat. 2, 97-117.
9. Hall, P. (1992). Effect of bias estimation on coverage accuracy of bootstrap confidence intervals for a probability density. Ann. Statist. 20, 675-694.
10. Härdle, W. and Bowman, A. W. (1988). Bootstrapping in nonparametric regression: local adaptive smoothing and confidence bands. J. Amer. Stat. Assoc. 83, 102-110.
11. Härdle, W., Huet, S., Mammen, E. and Sperlich, S. (2004). Bootstrap inference in semiparametric generalized additive models. Economet. Theor. 20, 265-300.
12. Härdle, W. and Marron, J. S. (1991). Bootstrap simultaneous error bands for nonparametric regression. Ann. Statist. 19, 778-796.
13. Hastie, T. and Tibshirani, R. (1990). Generalized additive models. Chapman and Hall, London.
14. Kauermann, G. and Opsomer, J. D. (2003). Local likelihood estimation in generalized additive models. Scand. J. Statist. 30, 317-337.
15. McCullagh, P. and Nelder, J. A. (1989). Generalized linear models. Chapman and Hall, London.
16. Nychka, D. (1988). Bayesian confidence intervals for smoothing splines. J. Amer. Statist. Assoc. 83, 1134-1143.
17. Ruppert, D., Wand, M. P. and Carroll, R. J. (2003). Semiparametric regression. Cambridge University Press, London.
18. Silverman, B. W. (1985). Some aspects of the spline smoothing approach to non-parametric regression curve fitting. J. Roy. Statist. Soc. B Met. 47, 1-52.
19. Wahba, G. (1983). Bayesian 'confidence intervals' for the cross-validated smoothing spline. J. Roy. Statist. Soc. B Met. 45, 133-150.
20. Wang, Y. and Wahba, G. (1995). Bootstrap confidence intervals for smoothing splines and their comparison to bayesian confidence intervals. J. Statist. Comput. Sim. 51, 263-279.
21. Wood, S. N. (2000). Modelling and smoothing parameter estimation with multiple quadratic penalties. J. Roy. Statist. Soc. B Met. 62, 413-428.
22. Wood, S. N. (2003). Thin plate regression splines. J. Roy. Statist. Soc. B Met. 65, 95-114.
23. Wood, S. N. (2004). Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Amer. Stat. Assoc. 99, 673-686.
24. Wood, S. N. (2006a). Generalized additive models: an introduction with R. Chapman and Hall, London.
25. Wood, S. N. (2006b). On confidence intervals for generalized additive models based on penalized regression splines. Aust. N. Z. J. Statist. 48, 445-464.
26. Wood, S. N. (2008). Fast stable direct fitting and smoothness selection for generalized additive models. J. Roy. Statist. Soc. B Met. 70, 495-518.