Generalized additive models

Statistical Science

Volumn 1, Issue 3, 1986, Pages 297-310

  Hastie, Trevor ^a   Tibshirani, Robert ^b,c  

^a LUCENT TECHNOLOGIES   (United States)

^b Faculty Award Fellow   (Canada)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Generalized linear models; Nonlinearity; Nonpara metric regression; Partial residuals; Smoothing

Indexed keywords

EID: 84972488102     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1177013604     Document Type: Article

References (31)

1. BREIMAN, L. and FRIEDMAN, J. H. (1985). Estimating optimal transformations for multiple regression and correlation. J. Amer. Statist. Assoc. 80 580-597.
2. BRILLINGER, D. (1977). Discussion of Consistent nonparametric regression, by C. J. Stone. Ann. Statist. 5 622-623.
3. CLEVELAND, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. J. Amer. Statist. Assoc. 74 829-836.
4. COX, D. R. (1972). Regression models and life tables. J. Roy. Statist. Soc. Ser. B 34 187-202.
5. FIENBERG, S. and GONG, G. (1984). Discussion of Graphical methods for assessing logistic regression models, by J. M. Landwehr, D. Pregibon, and A. C. Shoemaker. J. Amer. Statist. Assoc. 79 72-77.
6. FRIEDMAN, J. H. and STUETZLE, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc. 76 817-823.
7. FRIEDMAN, J. H. and STUETZLE, W. (1982). Smoothing of scatterplots. Tech. Rept. Orion 3, Dept, of Statistics, Stanford Univ.
8. FRIEDMAN, J. H. and TIBSHIRANI, R. (1984). The monotone smoothing of scatterplots. Technometrics 26 243-250.
9. GREEN, P. J. (1984). Iteratively reweighted least squares for maximum likelihood estimation and some robust and resistant alternatives (with discussion). J. Roy. Statist. Soc. Ser. B 46 149-192.
10. GREEN, P. J. and YANDELL, B. (1985). Semi-parametric generalized linear models. In Generalized Linear Models. Lecture Notes in Statist. (R. Gilchrist, B. Francis, and J. Whittaker, eds.) 32 44-55. Springer, New York.
11. HABERMAN, S. J. (1976). Generalized residuals for log-linear models. Proc. 9th Int. Biometrics Conference, Boston, 104-122, Biometric Soc., Raleigh, N.C.
12. HASTIE, T. (1984a). Discussion of Graphical methods for assessing logistic regression models, by J. M. Landwehr, D. Pregibon, and A. C. Shoemaker. J. Amer. Statist Assoc. 79 77-78.
13. HASTIE, T. (1984b). Principal curves and surfaces. Tech. Rept. Orion 24 and unpublished Ph.D. dissertation, Dept, of Statistics, Stanford Univ.
14. HASTIE, T. and TIBSHIRANI, R. (1984). Generalized additive models. Tech. Rept. 98, Dept, of Statistics, Stanford Univ.
15. HASTIE, T. and TIBSHIRANI, R. (1985a). Generalized additive models: some applications. In Generalized Linear Models. Lecture Notes in Statist. (R. Gilchrist, B. Francis, and J. Whittaker, eds.) 32 66-81. Springer, New York.
16. HASTIE, T. and TIBSHIRANI, R. (1985b). Smoothing in likelihood-based regression models. Tech. Rept. 1985-002, Dept, of Preventive Medicine and Biostatistics, Univ. of Toronto.
17. LANDWEHR, J. M., PREGIBON, D. and SHOEMAKER, A. C. (1984). Graphical methods for assessing logistic regression models (with discussion). J. Amer. Statist. Assoc. 79 61-81.
18. MCCULLAGH, P. (1980). Regression models for ordinal data. J. Roy. Statist. Soc. Ser. B 42 109-142.
19. MCCULLAGH, P. and NELDER, J. (1983). Generalized Linear Models. Chapman and Hall, London.
20. MILLER, R. G. and HALPERN, J. (1982). Regression with censored data. Biometrika 69 521-531.
21. NELDER, J. A. and WEDDERBURN, R. W. M. (1972). Generalized linear models. J. Roy. Statist. Soc. Ser. A 135 370-384.
22. O’SULLIVAN, F., YANDELL, B. and RAYNOR, W. (1984). Automatic smoothing of regression functions in generalized linear models. Tech. Rept. 734, Dept, of Statistics, Univ. of Wisconsin, Madison.
23. OWEN, A. (1983). The estimation of smooth curves. Unpublished manuscript.
24. REINSCH, C. (1967). Smoothing by spline functions. Numer. Math. 10 177-183.
25. SILVERMAN, B. W. (1985). Some aspects of the spline smoothing approach to nonparametric regression curve fitting (with discussion). J. Roy. Statist. Soc. Ser. B 47 1-52.
26. STONE, C. J. (1986). The dimensionality reduction principle for generalized additive models. Ann. Statist. 14 590-606.
27. STONE, C. J. and KOO, C.-Y. (1986a). Additive splines in statistics. Proc. Statist. Comp. Sect. Amer. Statist. Assoc.
28. TIBSHIRANI, R. (1984). Local likelihood estimation. Stanford technical report and unpublished Ph.D. dissertation, Dept, of Statistics, Stanford Univ.
29. WAHBA, G. (1980). Spline bases, regularization, and generalized cross-validation for solving approximation problems with large quantities of noisy data. Proc. Conf. on Approximation Theory in Honour of George Lorenz, Jan. 8-10, Austin, Texas (W. Chaney, ed.). Academic, New York.
30. WAHBA, G. and WOLD, S. (1975). A completely automatic French curve: Fitting spline functions by cross-validation. Comm. Statist. 4 1-7.
31. YOUNG, F. W., TAKANE, Y. and DE LEUUW, J. (1978). The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features. Psychometrika 43 279-282.