Generalized functional linear models with semiparametric single-index interactions

Journal of the American Statistical Association

Volumn 105, Issue 490, 2010, Pages 621-633

  Li, Yehua ^a   Wang, Naisyin ^b   Carroll, Raymond J ^c  

^a UNIVERSITY OF GEORGIA   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Functional data analysis; Generalized linear models; Interactions; Latent variables; Local estimating equation; Principal components; Single index models

Indexed keywords

EID: 78649440047     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2010.tm09313     Document Type: Article

References (27)

1. Baladandayuthapani, V., Mallick, B., Hong, M., Lupton, J., Turner, N., and Carroll, R. J. (2008), "Bayesian Hierarchical Spatially Correlated Functional Data Analysis With Application to Colon Carcinogenesis," Biometrics, 64, 64-73. [627]
2. Cai, T., and Hall, P. (2006), "Prediction in Functional Linear Regression," The Annals of Statistics, 34, 2159-2179. [621]
3. Capra, W. B., and Müller, H. G. (1997), "An Accelerated-Time Model for Response Curves," Journal of the American Statistical Association, 92, 72-83. [624]
4. Cardot, H., and Sarda, P. (2005), "Estimation in Generalized Linear Models for Functional Data via Penalized Likelihood," Journal of Multivariate Analysis, 92, 24-41. [621]
5. Carroll, R. J., Fan, J., Gijbels, I., andWand, M. P. (1997), "Generalized Partially Linear Single-Index Models," Journal of the American Statistical Association, 92 (438), 477-489. [622-624,626]
6. Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006), Measurement Error in Nonlinear Models: A Model Perspective (2nd ed.), New York: Chapman & Hall. [626]
7. Crainiceanu, C. M., Staicu, A., and Di, C. (2009), "Generalized Multilevel Functional Regression," Journal of the American Statistical Association, 104, 1550-1561. [621]
8. Di, C., Crainiceanu, C. M., Caffo, B. S., and Punjabi, N. M. (2009), "Multilevel Functional Principal Component Analysis," The Annals of Applied Statistics, 3, 458-488. [621]
9. Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis: Theory and Practice, New York: Springer-Verlag. [621]
10. Hall, P., and Hosseini-Nasab, M. (2006), "On Properties of Functional Principal Components Analysis," Journal of the Royal Statistical Society, Ser. B, 68, 109-126. [621,625,626]
11. Hall, P.,Müller, H.-G., andWang, J.-L. (2006), "Properties of Principal Component Methods for Functional and Longitudinal Data Analysis," The Annals of Statistics, 34, 1493-1517. [624,625,631]
12. Li, E., Li, Y., Wang, N.-Y., and Wang, N. (2008), "Functional Latent Feature Models for Data With Longitudinal Covariate Processes," preprint. [631]
13. Li, K. C. (1991), "Sliced Inverse Regression for Dimension Reduction" (with discussion), Journal of the American Statistical Association, 86, 316-342. [624]
14. Li, R., and Liang, H. (2008), "Variable Selection in Semiparametric Regression Modeling," The Annals of Statistics, 36, 261-286. [629]
15. Li, Y., Wang, N., Hong, M., Turner, N., Lupton, J., and Carroll, R. J. (2007), "Nonparametric Estimation of Correlation Functions in Spatial and Longitudinal Data,With Application to Colon Carcinogenesis Experiments," The Annals of Statistics, 35, 1608-1643. [627]
16. Liang, H., Qin, Y. S., Zhang, X. Y., and Ruppert, D. (2009), "Empirical- Likelihood-Based Inferences for Generalized Partially Linear Models," Scandinavian Journal of Statistics, 36, 433-443. [629]
17. McCullagh, P., and Nelder, J. A. (1989), Generalized Linear Models (2nd ed.), New York: Chapman & Hall. [622]
18. Morris, J. S., Vannucci, M., Brown, P. J., and Carroll, R. J. (2003), "Wavelet- Based Nonparametric Modeling of Hierarchical Functions in Colon Carcinogenesis, Journal of the American Statistical Association, 98 (463), 573- 583. [627]
19. Morris, J. S., Wang, N., Lupton, J. R., Chapkin, R. S., Turner, N. D., Hong, M. Y., and Carroll, R. J. (2001), "Parametric and Nonparametric Methods for Understanding the Relationship Between Carcinogen-Induced DNA Adduct Levels in Distal and Proximal Regions of the Colon," Journal of the American Statistical Association, 96, 455, 816-826. [627]
20. Müller, H.-G., and Stadtmüller, U. (2005), "Generalized Functional Linear Models," The Annals of Statistics, 33, 774-805. [621,622,626]
21. Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis (2nd ed.), New York: Springer-Verlag. [621]
22. Rice, J., and Silverman, B. (1991), "Estimating the Mean and Covariance Structure Nonparametrically When the Data Are Curves," Journal of the Royal Statistical Society, Ser. B, 53, 233-243. [624]
23. Xia, Y., and Härdle,W. (2006), "Semi-Parametric Estimation of Partially Linear Single-Index Models," Journal of Multivariate Analysis, 97, 1162-1184. [623,624]
24. Xia, Y., Tong, H., Li, W. K., and Zhu, L. (2002), "An Adaptive Estimation of Dimension Reduction Space" (with discussion), Journal of the Royal Statistical Society, Ser. B, 64, 363-410. [621,623,624]
25. Yao, F., Müller, H. G., and Wang, J. L. (2005), "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, 100, 577-590. [621,622,624,631] (Pubitemid 40816595)
26. Zhang, J.-T., and Chen, J. (2007), "Statistical Inferences for Functional Data," The Annals of Statistics, 35, 1052-1079. [625]
27. Zhou, L., Huang, J. Z., and Carroll, R. J. (2008), "Joint Modeling of Paired Sparse Functional Data Using Principal Components," Biometrika, 95 (3), 601-619. [622]