Efficient estimation for semivarying-coefficient models

Biometrika

Volumn 91, Issue 3, 2004, Pages 661-681

  Xia, Yingcun ^a   Zhang, Wenyang ^b   Tong, Howell ^c  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF KENT   (United Kingdom)

^c UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Efficient estimator; Local linear; Semivarying coefficient model; Strong mixing; Varying coefficient model

Indexed keywords

EID: 24944545692     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/91.3.661     Document Type: Article

References (38)

1. AKAIKE, H. (1973). Information theory and an extension of the maximum likelihood principle. In 2nd International Symposium on Information Theory, Ed. B. N. Petrov and F. Czáki, pp. 276-81. Budapest: Akademiai Kiadó.
2. ANDERSON, R. M. & MAY, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press.
3. BAILEY, N. T. J. (1975). The Mathematical Theory of Infectious Diseases and its Applications. London: Griffin.
4. BREIMAN, L. & FRIEDMAN, J. H. (1985). Estimating optimal transformations for multiple regression and correlation (with Discussion). J. Am. Statist. Assoc. 80, 580-619.
5. CARROLL, R. J., FAN, J., GUBELS, I. & WAND, M. P. (1997). Generalized partially linear single-index models. J. Am. Statist. Assoc. 92, 477-89.
6. CHEN, R. & TSAY, R. S. (1993). Functional-coefficient autoregressive models. J. Am. Statist. Assoc. 88, 298-308.
7. CHENG, B. & TONG, H. (1992). On consistent nonparametric order determination and chaos (with Discussion). J. R. Statist. Soc. B 54, 427-49.
8. DURLAUF, S. N. (2001). Manifesto for a growth econometrics. J. Economat. 100, 65-9.
9. ELLNER, S. P., BAILEY, B. A., BOBASHEV, G. V., GALLANT, A. R., GRENFELL, B. T. & NYCHKA, D. W. (1998). Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling. Am. Naturalist 151, 425-40.
10. ENGLE, R. F., GRANGER, C. W. J., RICE, J. & WEISS, A. (1986). Semiparametric estimates of the relation between weather and electricity. J. Am. Statist. Assoc. 81, 310-20.
11. FAN, J. & GUBELS, I. (1996). Local Polynomial Modelling and its Applications. London: Chapman and Hall.
12. FAN, J. & ZHANG, J. T. (2000). Functional linear models for longitudinal data. J. R. Statist. Soc. B 62, 303-22.
13. FAN, J. & ZHANG, W. (1999). Statistical estimation in varying coefficient models. Ann. Statist. 27, 1491-518.
14. FAN, J. & ZHANG, W. (2000). Simultaneous confidence bands and hypothesis testing in varying-coefficient models. Scand. J. Statist. 27, 715-31.
15. FAN, J., HÄRDLE, W. & MAMMEN, E. (1998). Direct estimation of additive and linear components for high dimensional data. Ann. Statist. 26, 943-71.
16. FAN, J., YAO, Q. & CAI, Z. (2003). Adaptive varying-coefficient linear models. J. R. Statist. Soc. B 65, 57-80.
17. FINKENSTÄDT, B. F. & GRENFELL, B. T. (2000). Time series modelling of childhood diseases: a dynamical systems approach. Appl. Statist. 49, 187-205.
18. FRIEDMAN, J. H. (1991). Multivariate adaptive regression splines (with Discussion). Ann. Statist. 19, 1-141.
19. GREEN, P. J. & SILVERMAN, B. W. (1994), Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. London: Chapman and Hall.
20. GU, C. & WAHBA, G. (1993). Smoothing spline ANOVA with component-wise Bayesian 'confidence intervals'. J. Camp. Graph. Statist. 2, 97-117.
21. HANNAN, E. J. & QUINN, B. G. (1979). The determination of the order of an autoregression. J. R. Statist. Soc. B 41, 190-5.
22. HÄRDLE, W. & MARRON, J. S. (1985). Optimal bandwidth selection in nonparametric regression function estimation. Ann. Statist. 13, 1465-81.
23. HÄRDLE, W., HALL, P. & ICHIMURA, H. (1993). Optimal smoothing in single-index models. Ann. Statist. 21, 157-78.
24. HASTIE, T. J. & TIBSHIRANI, R. (1990). Generalized Additive Models. London: Chapman and Hall.
25. HASTIE, T. J. & TIBSHIRANI, R. J. (1993). Varying-coefficient models (with Discussion). J. R. Statist. Soc. B 55, 757-96.
26. HECKMAN, J., ICHIMURA, H., SMITH, J. & TODD, P. (1998). Characterizing selection bias using experimental data. Econometrica 66, 1017-98.
27. HOOVER, D. R., RICE, J. A., WU, C. O. & YANG, L. P. (1998). Nonpararaetric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85, 809-22.
28. LI, K.-C. (1991). Sliced inverse regression for dimension reduction (with Discussion). J. Am. Statist. Assoc. 86, 316-42.
29. LIU, W. & LEVIN, S. A. (1986). Influence of nonlinear incidence rate upon the behaviour of SIRS epidemiological models. J. Math. Biol. 23, 187-204.
30. MASRY, E. (1996). Multivariate local polynomial regression for time series: uniform strong consistency and rates. J. Time Ser. Anal. 17, 571-99.
31. SCHWARTZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6, 461-4.
32. SMITH, R. L., DAVIS, J. M. & SPECKMAN, P. (1999). Assessing the human health risk of atmospheric particles. In Environmental Statistics: Analysing Data for Environmental Policy, Novartis Foundation Symposium 220, Ed. V. Barnett, A. Stein and K. F. Turkman, pp. 91-115. John Wiley & Sons.
33. SPECKMAN, P. (1998). Kernel smoothing in partial linear models. J. R. Statist. Soc. B 50, 413-36.
34. STONE, C. J., HANSEN, M., KOOPERBERG, C. & TRUONG, Y. K. (1997). Polynomial splines and their tensor products in extended linear modeling (with Discussion). Ann. Statist. 25, 1371-470.
35. STONE, M. (1977). Asymptotics for and against cross-validation. Biometrika 64, 29-35.
36. WAHBA, G. (1984), Partial spline models for semiparametric estimation of functions of several variables. In Statistical Analysis of Time Series, Proceedings of the Japan U.S. Joint Seminar, Tokyo, pp. 319-29. Tokyo: Institute of Statistical Mathematics.
37. XIA, Y. & LI, W. K. (1999). On the estimation and testing of functional-coefficient linear models. Statist. Sinica 9, 735-58.
38. XIA, Y., TONG, PL, LI, W. K. & ZHU, L. (2002). An adaptive estimation of dimension reduction space (with Discussion). J. R. Statist. Soc. B 64, 363-410.