Efficient semiparametric regression for longitudinal data with nonparametric covariance estimation

Biometrika

Volumn 98, Issue 2, 2011, Pages 355-370

  Li, Yehua ^a  

^a UNIVERSITY OF GEORGIA   (United States)

Author keywords

Covariance estimation; Functional data analysis; Generalized estimating equation; Kernel method; Partially linear model; Profile estimator

Indexed keywords

EID: 79957829938     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asq080     Document Type: Article

References (23)

1. BRUMBACK, B. A. & RICE, J. A. (1998). Smoothing spline models for the analysis of nested and crossed samples of curves. J. Am. Statist. Assoc. 93, 961-76. (Pubitemid 128384617)
2. DIGGLE, P. J. & VERBYLA, A. P. (1998). Nonparametric estimation of covariance structure in longitudinal data. Biometrics 54, 401-15. (Pubitemid 28262466)
3. DIGGLE, P. J.,HEAGERTY, P., LIANG, K.-Y., & ZEGER, S. L. (2002). Analysis of Longitudinal Data, 2nd ed. New York: Oxford University Press.
4. FAN, J. & JIANG, J. (2005). Nonparametric inferences for additive models. J. Am. Statist. Assoc. 100, 890-907. (Pubitemid 41276335)
5. FAN, J.&WU, Y. (2008). Semiparametric estimation of covariance matrixes for longitudinal data. J. Am. Statist. Assoc. 103, 1520-33.
6. FAN, J., HUANG, T. & LI, R. (2007). Analysis of longitudinal data with semiparametric estimation of covariance function. J. Am. Statist. Assoc. 102, 632-42.
7. HALL, P., FISHER, N. I. & HOFFMAN, B. (1994). On the nonparametric estimation of covariance functions. Ann. Statist. 22, 2115-34.
8. HALL, P.,MÜLLER, H. G. & WANG, J. L. (2006). Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist. 34, 1493-517. (Pubitemid 44231170)
9. HALL, P., MÜLLER, H. G. & YAO, F. (2008). Modelling sparse generalized longitudinal observations with latent Gaussian processes. J. R. Statist. Soc. B. 70, 703-23.
10. HENRY, K.,ERICE, A.,TIERNEY, C.,BALFOUR, H. H. JR, FISCHL, M. A.,KMACK, A.,LIOU, S. H.,KENTON, A.,HIRSCH, M. S., PHAIR, J.,MARTINEZ, A. & KAHN J. O. (1998). A randomized, controlled, double-blind study comparing the survival benefit of four different reverse transcriptase inhibitor therapies (three-drug, two-drug, and alternating drug) for the treatment of advanced AIDS. J. Acq. Immune Defic. Synd. Hum. Retrovir., 19, 339-49.
11. HUANG, J. Z., LIU, L., & LIU, N. (2007). Estimation of large covariance matrices of longitudinal data with basis function approximations. J. Comp. Graph. Statist. 16, 189-209.
12. LI, Y.,WANG, N.,HONG, M., TURNER, N., LUPTON, J. & CARROLL, R. J. (2007). Nonparametric estimation of correlation functions in spatial and longitudinal data, with application to colon carcinogenesis experiments. Ann. Statist. 35, 1608-43.
13. LIN, X. & CARROLL, R. J. (2001). Semiparametric regression for clustered data using generalized estimating equations. J. Am. Statist. Assoc. 96, 1045-56.
14. LIN, X. & CARROLL, R. J. (2006). Semiparametric estimation in general repeated measures problems. J. R. Statist. Soc. B 68, 69-88. (Pubitemid 43415336)
15. LIN, X.,WANG, N.,WELSH, A. H. & CARROLL, R. J. (2004). Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data. Biometrika, 91, 177-93. (Pubitemid 41309845)
16. MACK, Y. P. & SILVERMAN, B. W. (1982). Weak and strong uniform consistency of kernel regression estimates. Z. Wahr. verw. Geb. 61, 405-15.
17. MASRY, E. (1995). Multivariate local polynomial regression for time series: Uniform strong consistency and rates. J. Time Ser. Anal. 17, 571-599. (Pubitemid 126449848)
18. RICE, J. A. & SILVERMAN, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Statist. Soc. B 53, 233-43.
19. WANG, N. (2003). Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika, 90, 43-52. (Pubitemid 39047180)
20. WANG, N., CARROLL, R. J. & LIN, X. (2005). Efficient semiparametric marginal estimation for longitudinal/clustered data. J. Am. Statist. Assoc., 100, 147-57. (Pubitemid 40366825)
21. WU, W. B., & POURAHMADI, M. (2003). Nonparametric estimation of large covariance matrices of longitudinal data. Biometrika, 90, 831-44. (Pubitemid 39047122)
22. YAO, F.,MÜLLER, H. G. & WANG, J. L. (2005). Functional data analysis for sparse longitudinal data. J. Am. Statist. Assoc., 100, 577-90. (Pubitemid 40816595)
23. ZEGER, S. L. & DIGGLE, P. J. (1994). Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics 50, 689-99. (Pubitemid 24320817)