Asymptotic Properties of Backfitting Estimators

Journal of Multivariate Analysis

Volumn 73, Issue 2, 2000, Pages 166-179

  Opsomer, Jean D ^a  

^a E005A Lagomarcino Hall   (United States)

Author keywords

Additive model; Existence; Local polynomial regression; Optimal rates

Indexed keywords

EID: 0000982463     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1999.1868     Document Type: Article

References (19)

1. Ansley C. F., Kohn R. Convergence of the backfitting algorithm for additive models. J. Austral. Math. Soc. (Ser. A). 57:1994;316-329.
2. Buja A., Hastie T. J., Tibshirani R. J. Linear smoothers and additive models. Ann. Statist. 17:1989;453-555.
3. Chambers J. M., Hastie T. J. Statistical models in S. 1992;Wadsworth and Brooks/Cole, Pacific Grove.
4. Fan J., Härdle W., Mammen E. Direct estimation of low-dimensional components in additive models. Ann. Statist. 26:1998;943-971.
5. Friedman J. H., Stuetzle W. Projection pursuit regression. J. Amer. Statist. Assoc. 76:1981;817-823.
6. Gu C., Bates D. M., Chen Z., Wahba G. The computation of gcv functions through householder tridiagonalization with application to the fitting of interaction spline models. SIAM J. Matrix Anal. Appl. 10:1989;457-480.
7. Härdle W., Hall P. On the backfitting algorithm for additive regression models. Statist. Neerlandica. 47:1993;43-57.
8. Hastie T. J., Tibshirani R. J. Generalized Additive Models. 1990;Chapman and Hall, Washington.
9. N. W. Hengartner, Rate optimal estimation of additive regression via the integration method, preprint, Department of Statistics, Yale University, 1996.
10. Horn R. A., Johnson C. A. Matrix Analysis. 1985;Cambridge University Press, Cambridge.
11. O. B. Linton, E. Mammen, and, J. P. Nielsen, A kernel method of estimating structured nonparametric regression based on marginal estimation, preprint, 1997.
12. Linton O. B., Nielsen J. P. A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika. 82:1995;93-100.
13. Matlab Reference Guide. 1994;The MathWorks Inc. Natick.
14. Opsomer J.-D. Optimal Bandwidth Selection for Fitting an Additive Model by Local Polynomial Regression. 1995;Cornell University.
15. Opsomer J.-D., Ruppert D. Fitting a bivariate additive model by local polynomial regression. Ann. Statist. 25:1997;186-211.
16. Opsomer J.-D., Ruppert D. A fully automated bandwidth selection method for fitting additive models by local polynomial regression. J. Amer. Statist. Assoc. 93:1998;605-619.
17. Ruppert D., Wand M. P. Multivariate locally weighted least squares regression. Ann. Statist. 22:1994;1346-1370.
18. Stone C. J. Additive regression and other nonparametric models. Ann. Statist. 13:1985;689-705.
19. Wahba G. Partial and interaction splines for the semiparametric estimation of functions of several variables. Boardman T. J. Comput. Sci. and Stat.: Proceedings of the 18th Symp. on the Interface. 1986;75-80 American Statistical Association.