Smooth backfitting in practice

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

Volumn 67, Issue 1, 2005, Pages 43-61

  Nielsen, Jens Perch ^a   Sperlich, Stefan ^b  

^a Research Department   (Denmark)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Backfitting; Bandwidth choice; Computational statistics; Cross validation; Nonparametric estimation

Indexed keywords

EID: 12844274407     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2005.00487.x     Document Type: Article

References (21)

1. Buja, A., Hastie, T. and Tibshirani, R. (1989) Linear smoothers and additive models (with discussion). Ann. Statist., 17, 453-555.
2. Deaton, A. and Muellbauer, J. (1980) Economics and Consumer Behavior. Cambridge: Cambridge University Press.
3. Dette, H., von Lieres, C. und Wilkau and Sperlich, S. (2004) A comparison of different nonparametric methods for inference on additive models. J. Nonparam. Statist., to be published.
4. Härdle, W., Hall, P. and Marron, J. S. (1988) How far are automatically chosen regression smoothing parameters from their optimum (with discussion)? J. Am. Statist. Ass., 83, 86-101.
5. Hastie, T. J. and Tibshirani, R. J. (1990) Generalized Additive Models. London: Chapman and Hall.
6. Hengartner, N. W. and Sperlich, S. (2001) Rate optimal estimation with the integration method in the presence of many covariates. Technical Report. University Carlos III de Madrid, Madrid.
7. Linton, O. B. (1997) Efficient estimation of additive nonparametric regression models. Biometrika, 84, 469-473.
8. Linton, O. B. and Nielsen, J. P. (1995) A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika, 82, 93-101.
9. Mammen, E., Linton, O. B. and Nielsen, J. P. (1999) The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Ann. Statist., 27, 1443-1490.
10. Mammen, E., Marron, J. S. Turlach, B. and Wand, M. P. (2001) A general projection framework for constrained smoothing. Statist. Sci., 16, 232-248.
11. Mammen, E. and Nielsen, J. P. (2003) Generalised structured models. Biometrika, 90, 551-566.
12. Mammen, E. and Park, B. U. (2004) Bandwidth selection for smooth backfitting in additive models. Ann. Statist., to be published.
13. Newey, W. K. (1994) Kernel estimation of partial means. Econometr. Theory, 10, 233-253.
14. Nielsen, J. P. and Linton, O. B. (1998) An optimization interpretation of integration and back-fitting estimators for separable nonparametric models. J. R. Statist. Soc. B, 60, 217-222.
15. Opsomer, J. D. (2000) Asymptotic properties of backfitting estimators. J. Multiv. Anal., 73, 166-179.
16. Opsomer, J. D. and Ruppert, D. (1997) Fitting a bivariate additive model by local polynomial regression. Ann. Statist., 25, 186-211.
17. Sperlich, S. (1998) Additive Modelling and testing Model Specification. Aachen: Shaker.
18. Sperlich, S., Linton, O. B. and Härdle, W. (1999) Integration and backfitting methods in additive models: finite sample properties and comparison. Test, 8, 419-458.
19. Sperlich, S., Tjøstheim, D. and Yang, L. (2002) Nonparametric estimation and testing of interaction in additive models. Econometr. Theory, 18, 197-251.
20. Stone, C. J. (1985) Additive regression and other nonparametric models. Ann. Statist., 13, 689-705.
21. Tjøstheim, D. and Auestad, B. H. (1994) Nonparametric identification of nonlinear time series: projections. J. Am. Statist. Ass., 89, 1398-1409.