Estimation of additive regression models with known links

Biometrika

Volumn 83, Issue 3, 1996, Pages 529-540

  Linton, O B ^a   Hardle W ^b  

^a YALE UNIVERSITY   (United States)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Additive regression model; Dimensionality reduction; Kernel estimation; Nonparametric regression

Indexed keywords

EID: 0000346456     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/83.3.529     Document Type: Article

References (26)

1. BREIMAN, L. & FRIEDMAN, J. H. (1985). Estimating optimal transformations for multiple regression and correlation (with Discussion). J. Am. Statist, Assoc. 80, 580-619.
2. BUJA, A., HASTIE, T. & TIBSHIRANI, R. (1989). Linear smoothers and additive models (with Discussion). Ann. Statist. 17, 453-555.
3. Cox, D. R. (1983). Some remarks on overdispersion. Biometrika 70, 269-74.
4. CUZICK, J. (1992). Efficient estimates in semiparametric additive regression models with unknown error distribution. Ann. Statist. 20, 1129-36.
5. FAN, J. (1992). Design adaptive nonparametric regression. J. Am. Statist. Assoc. 87, 998-1004.
6. FAN, J., HECKMAN, N. & WAND, M. (1995). Local polynomial kernel regression for generalised linear models and quasi-likelihood functions. J. Am. Statist. Assoc. 90, 141-50.
7. HALL, P. (1989). On projection pursuit regression. Ann. Statist. 17, 573-88.
8. HÄRDLE, W. (1990) Applied Nonparametric Regression, Econometric Monograph Series 19. Cambridge University Press.
9. HÄRDLE, W. & LINTON, O. B. (1995). Nonparametric regression. In Encyclopedia of the Statistical Sciences, 12, Ed. S. Kotz and C. Read, New York: John Wiley.
10. HÄRDLE, W. & MARRON, J. S. (1991). Bootstrap simultaneous errors bars for nonparametric regression. Ann. Statist. 19, 778-96.
11. HASTIE, T. & TIBSHIRANI, R. (1991). Generalised Additive Models. London: Chapman and Hall.
12. IBRAGIMOV, I. A. & HASMINSKII, R. Z. (1980). On nonparametric estimation of regression. Soviet Math. Dokl. 21, 810-4.
13. JONES, M. C. (1993). Do not weight for heteroskedasticity in nonparametric regression. Aust. J. Statist. 35, 89-92.
14. LEONTIEFF, W. (1947). Introduction to a theory of an internal structure of functional relationships. Econometrica 15, 361-73.
15. LINTON, O. B. & NIELSEN, J. P. (1995). Estimating structured nonparametric regression by the kernel method. Biometrika 82, 93-101.
16. MCCULLAGH, P. & NELDER, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman and Hall.
17. NEWEY, W. K. (1994). Kernel estimation of partial means. Economet. Theory 10, 233-53.
18. ROBINSON, P. M. (1988). Root-n consistent semiparametric regression. Econometrica 56, 931-54.
19. ROTHENBERG, T. J. (1972). Efficient Estimation with a Priori Information. New Haven, CT: Cowles Foundation.
20. SILVERMAN, B. W. (1978). Weak and strong uniform consistency of the kernel estimate of a density function and its derivatives. Ann. Statist. 6, 177-84.
21. STONE, C. J. (1980). Optimal rates of convergence for nonparametric estimators. Ann. Statist. 8, 1348-60.
22. STONE, C. J. (1982). Optimal global rates of convergence for nonparametric regression. Ann. Statist. 8, 1040-53.
23. STONE, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, 685-705.
24. STONE, C. J. (1986). The dimensionality reduction principle for generalised additive models. Ann. Statist. 14, 592-606.
25. TIBSHIRANI, R. & HASTIE, T. (1987). Local likelihood estimation. J. Am. Statist. Assoc. 82, 559-67.
26. TJØSTHEIM, D. & AUESTAD, B. (1994). Nonparametric identification of nonlinear time series: projections. J. Am. Statist. Assoc. 89, 1398-409.