Residual information criterion for single-index model selections

Journal of Nonparametric Statistics

Volumn 16, Issue 1-2, 2004, Pages 187-195

  Naik, P A ^a   Tsai, Chih Ling ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Local polynomial regression; Residual likelihood; Sliced inverse regression; Variable and smoothing estimator selections

Indexed keywords

EID: 0842264217     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485250310001624800     Document Type: Conference Paper

References (26)

1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. N. and Csaki, F. (Eds.), 2nd International Symposium on Information Theory. Akademia Kiado, Budapest, pp. 267-281.
2. Brillinger, D. R. (1983). A generalized linear model with "Gaussian" regressor variables. In: Bickel, P. J., Doksum, K. A. and Hodges, J. L. (Eds.), A Festschrift for Erich L. Lehmann in Honor of His Sixty-Fifth Birthday. Wadsworth, Belmont, pp. 97-114.
3. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference, 2nd ed. Springer, New York.
4. Carroll, R. J., Fan, J., Gijbels, I. and Wand, M. P. (1997). Generalized partially linear single-index models. J. Am. Statist. Assoc., 92, 477-489.
5. Chen, C. H. and Li, K. C. (1998). Can sir be a popular as multiple linear regression? Statistica Sinica, 8, 289-316.
6. Cleveland, W. S. and Devlin, S. J. (1988). Locally weighted regression: An approach to regression analysis by local fitting. J. Amer. Statist. Assoc., 83, 596-610.
7. Diggle, P. J., Liang, K. Y. and Zeger, S. L. (1994). Analysis of Longitudinal Data. Oxford University Press, New York.
8. Dolan, R. J. (1993). Managing the New Product Development Process. Addison Wesley, New York.
9. Duan, N. and Li, K. C. (1991). Slicing regression: A link free regression method. Ann. Statist., 19, 505-530.
10. Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications. Chapman and Hall, New York.
11. Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman and Hall, New York.
12. Horowitz, J. L. (1998). Semipammetric Methods in Econometrics. Springer, New York.
13. Hristache, M., Juditsky, A. and Spokoiny, V. (2001). Direct estimation of the index coefficient in a single-index model. Ann. of Statist., 29, 595-623.
14. Hurvich, C. M. and Tsai, C. L. (1989). Regression and time series model selection in small samples. Biometrika, 76, 297-307.
15. Hurvich, C. M., Simonoff, J. S. and Tsai, C. L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. J. R. Statist. Soc. B, 60, 271-293.
16. Ichimura, H. and Lee, L. F. (1991). Semiparametric least squares estimation of multiple index models: Single equation estimation. In: Barnett, W. A., Powell, J. and Tauchen, G. (Eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics. Cambridge University Press, Cambridge, pp. 3-49.
17. Linhart, H. and Zucchini, W. (1986). Model Selection. Wiley, New York.
18. McCullagh, P. and Neider, J. A. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, New York.
19. McQuarrie, A. D. R. and Tsai, C. L. (1998). Regression and Time Series Model Selection. World Scientific Publishing, Singapore.
20. Naik, P. A. and Tsai, C. L. (2001). Single-index model selections. Biometrika, 88, 821-832.
21. Powell, J. L., Stock, J. H. and Stoker, T. M. (1989). Semiparametric estimation of index coefficients. Econometrica, 57, 1403-1430.
22. Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist, 6, 461-464.
23. Shi, P. and Tsai, C. L. (2002). Regression model selection-a residual likelihood approach. J. R. Statist. Soc., 64, 237-252.
24. Simonoff, J. S. (1996). Smoothing Methods in Statistics. Springer, New York.
25. Verbyla, A. P. (1993). Modelling variance heterogeneity: Residual maximum likelihood and diagnostics. J. R. Statist. Soc., 55, 493-508.
26. Verbyla, A. P. (1990). A conditional derivation of residual maximum likelihood. Aust. J. Statist., 32, 227-230.