Polynomial splines and their tensor products in extended linearmodeling

Annals of Statistics

Volumn 25, Issue 4, 1997, Pages 1371-1470

  Stone, Charles J ^a   Hansen, Mark H ^c   Kooperberg, Charles ^b   Truong, Young K ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Fred Hutchinson Cancer Research Center   (United States)

^c LUCENT TECHNOLOGIES   (United States)

^d IL   (United States)

Author keywords

ANOVA; Density estimation; Generalized additive models; Generalized linear models; Least squares; Logistic regression; Maximum likelihood; Model selection; Multiple classification; Nonparametric regression; Optimal rates of convergence

Indexed keywords

EID: 0031484203     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (63)

1. ANDERSEN, P. K., BORGAN, Ø., GILL, R. D. and KEIDING, N. (1993). Statistical Models Based on Counting Processes. Springer, New York.
2. BELSEY, D. A., KUH, E. and WELSCH, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley, New York.
3. BOURLARD, H. A. and MORGAN, N. (1994). Connectionist Speech Recognition. Kluwer, Boston.
4. BOWIE, J. U., LUTHY, R. and EISENBERG, D. (1991). A method to identify protein sequences that fold into a known 3-dimensional structure. Science 253 164-170.
5. BREIMAN, L. (1993). Fitting additive models to regression data. Comput. Statist. Data Anal. 15 13-46.
6. BREIMAN, L., FRIEDMAN, J. H., OLSHEN, R. A. and STONE, C. J. (1984). Classification and Regression Trees. Wadsworth, Belmont, CA.
7. BRESLOW, N. E. (1972). Contribution to the discussion on the paper by D. R. Cox, Regression and life tables. J. Roy. Statist. Soc. Ser. B 34 216-217.
8. BRESLOW, N. E. (1974). Covariance analysis of censored survival data. Biometrics 30 89-99.
9. BRILLINGER, D. R. (1981). Time Series: Data Analysis and Theory. Holden-Day, San Francisco.
10. CHUI, C. K. (1988). Multivariate Splines. SIAM, Philadelphia.
11. 1 quadratic finite elements and vertex splines. Math. Comp. 54 169-187.
12. COLE, R., NOEL, M., BURNETT, D. C., FANTY, M., LANDER, T., OSHIKA, B. and SUTTON, S. (1994). Corpus development activities at the Center for Spoken Language Understanding. Technical report, CSLU, Portland, OR.
13. COLE, R. A., ROGINSKI, K. and FANTY, M. (1992). A telephone speech database of spelled and spoken names. In Proceedings of the International Conference on Spoken Language Processing 891-893. Quality Color Press, Univ. Alberta, Edmonton.
14. COX, D. R. (1972). Regression models and life tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187-220.
15. COX, D. R. and OAKES, D. (1984). Analysis of Survival Data. Chapman and Hall, London.
16. DE BOOR, C. (1978). A Practical Guide to Splines. Springer, New York.
17. DE BOOR, C. (1987). B-form basics. In Geometric Modeling (G. Farin, ed.) 131-148. SIAM, Philadelphia.
18. DURKA, P. J., KELLY, E. F. and Blinowska, K. J. (1995). Time-frequency analysis of stimulus-driven EEG activity by matching pursuit. In Proceedings of the 18th Annual Conference of the IEEE EMBS, Amsterdam, October 31-November 3, 1996. IEEE, New York.
19. FAMILY EXPENDITURE SURVEY (1968-1983). Annual base tapes and reports (1968-1983). Dept. Employment, Statistics Division, Her Majesty's Stationary Office, London.
20. FAN, J. and GIJBELS, I. (1996). Local Polynomial Modeling and Its Applications. Chapman and Hall, London.
21. FARIN, G. (1986). Triangular Bernstein-Bézier patches. Comput. Aided Geom. Design 3 83-127.
22. FLEMING, T. R. and HARRINGTON, D. P. (1991). Counting Processes and Survival Analysis. Wiley, New York.
23. FRIEDMAN, J. H. (1991). Multivariate adaptive regression splines (with discussion). Ann. Statist. 19 1-141.
24. FRIEDMAN, J. H. and SILVERMAN, B. W. (1989). Flexible parsimonious smoothing and additive modeling (with discussion). Technometrics 31 3-39.
25. GAUVAIN, J. L., LAMEL, L. F., ADDA, G. and ADDA-DECKER, M. (1994). Speaker-independent continuous speech dictation. Speech Communication 15 21-37.
26. GRAY, R. J. (1992). Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis. J. Amer. Statist. Assoc. 87 942-951.
27. GREEN, P. J. and SILVERMAN, B. W. (1994). Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman and Hall, London.
28. GU, G. and WAHBA, G. (1993). Smoothing spline ANOVA with component-wise Bayesian "confidence intervals." J. Comput. Graph. Statist. 2 97-117.
29. HANSEN, M. (1994). Extended linear models, multivariate splines and ANOVA. Ph.D. dissertation, Dept. Statistics, Univ. California, Berkeley.
30. HANSEN, M., KOOPERBERG, C. and SARDY, S. (1996). Triograms models. J. Amer. Statist. Assoc. To appear.
31. HASTIE, T. and TIBSHIRANI, R. (1990). Generalized Additive Models. Chapman and Hall, London.
32. HERMANSKY, H. (1990). Perceptual linear predictive (PLP) analysis of speech. Journal of the Acoustical Society of America 87 1738-1752.
33. HOBOHM, U., SCHARF, M., SCHNEIDER, R. and SANDER, C. (1992). Selection of representative protein data sets. Protein Science 1 409-417.
34. KALBFLEISCH, J. D. and PRENTICE, R. L. (1980). The Statistical Analysis of Failure Time Data. Wiley, New York.
35. KAPLAN, E. L. and MEIER, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 457-481.
36. KENNEDY, W. J. and GENTLE, J. E. (1980). Statistical Computing. Dekker, New York.
37. KOOPERBERG, C., BOSE, S. and STONE, C. J. (1997). Polychotomous regression. J. Amer. Statist. Assoc. 92 117-127.
38. KOOPERBERG, C. and STONE, C. J. (1991). A study of logspline density estimation. Comput. Statist. Data Anal. 12 327-347.
39. KOOPERBERG, C. and STONE, C. J. (1992). Logspline density estimation for censored data. J. Comput. Graph. Statist. 1 301-328.
40. KOOPERBERG, C., STONE, C. J. and TRUONG, Y. K. (1995a). Hazard regression. J. Amer. Statist. Assoc. 90 78-94.
41. 2 rate of convergence for hazard regression. Scand. J. Statist. 22 143-157.
42. KOOPERBERG, C., STONE, C. J. and TRUONG, Y. K. (1995c). Logspline estimation of a possibly mixed spectral distribution. J. Time Ser. Anal. 16 359-388.
43. KOOPERBERG, C., STONE, C. J. and TRUONG, Y. K. (1995d). Rate of convergence for logspline spectral density estimation. J. Time Ser. Anal. 16 389-401.
44. MCCULLAGH, P. and NELDER, J. A. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, London.
45. MILLER, R. G. (1981). Survival Analysis. Wiley, New York.
46. PARZEN, E. (1979). Nonparametric statistical data modeling. J. Amer. Statist. Assoc. 74 105-131.
47. RABINER, L. and JUANG, B.-H. (1993). Fundamentals of Speech Recognition. Prentice-Hall, Englewood Cliffs, NJ.
48. SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461-464.
49. SILVERMAN, B.W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
50. SLEEPER, L. A. and HARRINGTON, D. P. (1990). Regression splines in the Cox model with application to covariate effects in liver disease. J. Amer. Statist. Assoc. 85 941-949.
51. SMITH, P. L. (1982). Curve fitting and modeling with splines using statistical variable selection techniques. Report NASA 166034, NASA, Langley Research Center, Hampton, VA.
52. SOLVD INVESTIGATORS (1990). Studies of left ventricular dysfunction (SOLVD) - rationale, design, and methods: two trials that evaluate the effect of enalapril in patients with reduced ejection fraction. American Journal of Cardiology 6 315-322.
53. STONE, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13 689-705.
54. STONE, C. J. (1986). The dimensionality reduction principle for generalized additive models. Ann. Statist. 14 590-606.
55. STONE, C. J. (1990). Large-sample inference for log-spline models. Ann. Statist. 18 717-741.
56. STONE, C. J. (1991). Asymptotics for doubly flexible logspline response models. Ann. Statist. 19 1832-1854.
57. STONE, C. J. (1994). The use of polynomial splines and their tensor products in multivariate function estimation (with discussion). Ann. Statist. 22 118-184.
58. STONE, C. J. and KOO, C.-Y. (1986a). Additive splines in statistics. In Proceedings of the Statistical Computing Section 45-48. Amer. Statist. Assoc., Alexandria, VA.
59. STONE, C. J. and KOO, C.-Y. (1986b). Logspline density estimation. Contemp. Math. 59 1-15.
60. WAHBA, G. (1990). Spline Models for Observational Data. SIAM, Philadelphia.
61. WAND, M. P. and JONES, M. C. (1995). Kernel Smoothing. Chapman and Hall, London.
62. WAND, M. P., MARRON, S. J. and RUPPERT, D. (1991). Transformations in density estimation (with discussion) J. Amer. Statist. Assoc. 86 343-361.
63. ZHANG, K. and EISENBERG, D. (1994). The three-dimensional profile method using residue preference as a continuous function of residue environment. Protein Science 3 687-695.