A semiparametric model for cluster data

Annals of Statistics

Volumn 37, Issue 5 A, 2009, Pages 2377-2408

  Zhang, Wenyang ^a   Fan, Jianqing ^b   Sun, Yan ^c  

^a University of Bath   (United Kingdom)

^b Princeton University   (United States)

^c SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Cluster effect; Cluster level variable; Local linear modeling; Varying coefficient models

Indexed keywords

EID: 69049101184     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS662     Document Type: Article

References (32)

1. Bickel, P. L. and Rosenblatt, M. (1973). On some global measures of the derivations of density function estimates. Ann. Statist. 1 1071-1095. MR0348906
2. Brumback, B. and Rice, J. A. (1998). Smoothing spline models for the analysis of nested and crossed samples of curves (with discussion). J. Amer. Statist. Assoc. 93 961-994. MR1649194
3. Chiang, C.-T., Rice, J.A. and Wu, C. O. (2001). Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. J. Amer. Statist. Assoc. 96 605-619. MR1946428
4. Chiou, J.-M. and Muller, H.-G. (2005). Estimated estimating equations: Semiparametric inference for clustered/longitudinal data. J. Roy. Statist. Soc. Ser. B 67 531-553. MR2168203
5. Csörg̈, M. and Revesz, P. (1981). Strong Approximations in Probability and Statistics. Academic Press, New York. MR0666546
6. Diggle, P. J., Heagerty, P., Liang, K.Y. and Zeger, S. L. (2002). Analysis of Longitudinal Data. Oxford Univ. Press, London. MR2049007
7. Fan, J. and Gijbels, I. (1995). Data-driven bandwidth selection in local polynomial fitting: Variable bandwidth and spatial adaptation. J. Roy. Statist. Soc. Ser. B 57 371-394. MR1323345
8. Fan, J. and Li, R. (2004). New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. J. Amer. Statist. Assoc. 99 710-723. MR2090905
9. Fan, J. and Zhang, W. (1999). Statistical estimation in varying coefficient models. Ann. Statist. 27 1491-1518. MR1742497
10. Fan, J. and Zhang, W. (2000). Simultaneous confidence bands and hypothesis testing in varying-coefficient models. Scand. J. Statist. 27 715-731. MR1804172
11. Fan, J. and Wu, Y. (2008). Semiparametric estimation of covariance matrices for longitudinal data. J. Amer. Statist. Assoc. To appear.
12. Fan, J., Zhang, C. and Zhang, J. (2001). Generalized likelihood ratio statistics and Wilks phenomenon. Ann. Statist. 29 153-193. MR1833962
13. Hardle, W. (1989). Asymptotic maximal deviation of M-smoothers. J. Multivariate Anal. 29 163-179. MR1004333
14. Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85 809-822. MR1666699
15. Huang, J.Z., Wu, C.O. and Zhou, L. (2002). Varying-coefficient models and basis function approximations for the analysis of repeated measurements. Biometrika 89 111-128. MR1888349
16. Lam, C. and Fan, J. (2008). Profile-Kernel likelihood inference with diverging number of parameters. Ann. Statist. 36 2232-2260.
17. Li, R. and Liang, H. (2008). Variable selection in semiparametric regression modeling. Ann. Statist. 36 261-286. MR2387971
18. Lin, X. and Carroll, R. J. (2000). Nonparametric function estimation for clustered data when the predictor is measured without/with error. J. Amer. Statist. Assoc. 95 520-534. MR1803170
19. Lin, X. and Carroll, R. J. (2006). Semiparametric estimation in general repeated measures problems. J. Roy. Statist. Soc. Ser. B 68 69-88. MR2212575
20. Lin, Z.Y. and Lu, C. R. (1992). Strong Approximation Theorem. Science Press, Beijing, China. (In Chinese.)
21. Martinussen, T. and Scheike, T. H. (1999). A semiparametric additive regression model for longitudinal data. Biometrika 86 691-702. MR1723787
22. Mitra, S. N., Al-Sabir, A., Cross, A.R. and Jamil, K. (1997). Bangladesh and demographic health survey 1996-1997. National Institute of Population Research and Training (NIPORT), Mitra and Associates, and Macro International Inc., Dhaka and Calverton, MD.
23. Qu, A. and Li, R. (2006). Quadratic inference functions for varying-coefficient models with longitudinal data. Biometrics 62 379-391. MR2227487
24. Sun, Y., Zhang, W. and Tong, H. (2007). Estimation of the covariance matrix of random effects in longitudinal studies. Ann. Statist. 35 2795-2814. MR2382666
25. Wang, N. (2003). Marginal nonparametric kernel regression accounting within-subject correlation. Biometrika 90 43-52. MR1966549
26. Wang, N., Carroll, R. J. and Lin, X. (2005). Efficient semiparametric marginal estimation for longitudinal/clustered data. J. Amer. Statist. Assoc. 100 147-157. MR2156825
27. Welsh, A. H., Lin, X. and Carroll, R. J. (2002). Marginal longitudinal nonparametric regression: Locality and efficiency of spline and kernel methods. J. Amer. Statist. Assoc. 97 482-493. MR1941465
28. Wu, C.O., Chiang, C.T. and Hoover, D. R. (1998). Asymptotic confidence regions for kernel smoothing of a varying-coefficient model with longitudinal data. J. Amer. Statist. Assoc. 93 1388-1402. MR1666635
29. Xia, Y. (1998). Bias-corrected confidence bands in nonparametric regression. J. Roy. Statist. Soc.Ser. B 60 797-811. MR1649488
30. Xia, Y. and Li, W. K. (1999). On the estimation and testing of functional-coefficient linear models. Statist. Sinica 9 735-757. MR1711643
31. Zeger, S. L. and Diggle, P. J. (1994). Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics 50 689-699.
32. Zhang, W., Lee, S.Y. and Song, X. (2002). Local polynomial fitting in semivarying coefficient models, J. Multivariate Anal. 82 166-188. MR1918619