Bandwidth selection for smooth backfitting in additive models

Annals of Statistics

Volumn 33, Issue 3, 2005, Pages 1260-1294

  Mammen, Enno ^a   Park, Byeong U ^b  

^a UNIVERSITY OF MANNHEIM   (Germany)

^b Seoul National University   (South Korea)

Author keywords

Backfitting; Bandwidth selection; Local polynomial smoothing; Nadaraya Watson; Nonparametric regression; Penalized least squares; Plug in rules

Indexed keywords

EID: 23744448208     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000101     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. DE LA PEÑA, V. and GINÉ, E. (1999). Decoupling. From Dependence to Independence. Springer, New York.
3. FAN, J. and GIJBELS, I. (1996). Local Polynomial Modelling and Its Applications. Chapman and Hall, London.
4. HÄRDLE, W., HALL, P. and MARRON, J. S. (1988). How far are automatically chosen regression smoothing parameters from their optimum? (with discussion). J. Amer. Statist. Assoc. 83 86-101.
5. HASTIE, T. J. and TIBSHIRANI, R. J. (1990). Generalized Additive Models. Chapman and Hall, London.
6. HERRMANN, E. (2000). Variance estimation and bandwidth selection for kernel regression. In Smoothing and Regression: Approaches, Computation and Application (M. G. Schimek, ed.) 71-107. Wiley, Chichester.
7. JONES, M. C., MARRON, J. S. and SHEATHER, S. J. (1996). A brief survey of bandwidth selection for density estimation. J. Amer. Statist. Assoc. 91 401-407.
8. LINTON, O. and NIELSEN, J. P. (1995). A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika 82 93-100.
9. MAMMEN, E., LINTON, O. 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. NIELSEN, J. P. and SPERLICH, S. (2005). Smooth backfitting in practice. J. R. Stat. Soc. Ser. B Stat. Methodol. 67 43-61.
12. OPSOMER, J. D. (2000). Asymptotic properties of backfitting estimators. J. Multivariate Anal. 73 166-179.
13. OPSOMER, J. D. and RUPPERT, D. (1997). Fitting a bivariate additive model by local polynomial regression. Ann. Statist. 25 186-211.
14. OPSOMER, J. D. and RUPPERT, D. (1998). A fully automated bandwidth selection method for fitting additive models. J. Amer. Statist. Assoc. 93 605-619.
15. PARK, B. U. and MARRON, J. S. (1990). Comparison of data-driven bandwidth selectors. J. Amer. Statist. Assoc. 85 66-72.
16. PARK, B. U. and MARRON, J. S. (1992). On the use of pilot estimators in bandwidth selection. J. Nonparametr. Statist. 1 231-240.
17. PARK, B. U. and TURLACH, B. A. (1992). Practical performance of several data-driven bandwidth selectors (with discussion). Comput. Statist. 1 251-285.
18. RUPPERT, D., SHEATHER, S. J. and WAND, M. P. (1995). An effective bandwidth selector for local least squares regression. J. Amer. Statist. Assoc. 90 1257-1270.
19. SHEATHER, S. J. and JONES, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. J. Roy. Statist. Soc. Ser. B 53 683-690.
20. STONE, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13 689-705.
21. WOOD, S. N. (2000). Modelling and smoothing parameter estimation with multiple quadratic penalties. J. R. Stat. Soc. Ser. B Stat. Methodol. 62 413-428.