An overview on nonparametric and semiparametric techniques for longitudinal data

Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of his 65th Birthday

Volumn , Issue , 2006, Pages 277-303

  Fan, Jianqing ^a   Li, Runze ^b  

^a Princeton University   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967683993     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9781860948886_0013     Document Type: Chapter

References (79)

1. Altman, N. S. (1990). Kernel smoothing of data with correlated errors. Journal of American Statistical Association, 85, 749-759.
2. Antoniadis, A. and Fan, J. (2001). Regularization of wavelets approximations (with discussions). Journal of American Statistical Association, 96, 939- 967.
3. Berhane, K. and Tibshirani, R. J. (1998). Generalized additive models for longitudinal data. Canadian Journal of Statistics, 26, 517-535.
4. Cai, Z, Fan, J. and Li, R. (2000). Efficient estimation and inferences for varying- coefficient models. Journal of American Statistical Association, 95, 888- 902.
5. Carroll, R. J., Hall, P., Apanasovivh, T. V. and Lin, X. (2004). Histospline method in nonparametric regression models with application to clustered longitudinal data. Statistica Sinica, 14, 649-674.
6. Chiang, C.-T., Rice, J. A. and Wu, C. O. (2001). Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. Journal of American Statistical Association, 96, 605-619.
7. Daniels, M. J. and Kass, R. E. (2001). Shrinkage estimators for covariance matrices. Biometrics, 57, 1173-1184.
8. Daniels, M. J. and Pourahmadi, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data. Biometrika, 89, 553-566.
9. Diggle, P. J., Heagerty, P., Liang, K. Y., Zeger, S. L. (2002). Analysis of Longitudinal Data, 2nd Edition, Oxford, U. K. Oxford University Press.
10. Diggle, P. J. and Verbyla, A. P. (1998). Nonparametric estimation of covariance structure of longitudinal data. Biometrics, 54, 401-415.
11. Donoho, D. L. and Johnstone, I. M. (1994). Ideal spatial adaptation by wavelets shrinkage. Biometrika 81, 425-455.
12. Engle, R. F., Granger,C. W. J., Rice, J. A. and Weiss, A. (1986). Semiparametric estimates of the relation between weather and electricity sales. Journal of American Statistical Association, 81, 310-320.
13. Eubank, R. L., Huang, C. F., Maldonado, Y. M., Wang, N., Wang, S. and Buchanan, R. J. (2004). Smoothing spline estimation in varying- coefficient models Journal of Royal Statistical Society, Series B, 66, 653-667.
14. Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications, Chapman and Hall, London.
15. Fan, J., Heckman, N. E. and Wand, M. P. (1995). Local polynomial kernel regression for generalized linear models and quasi-likelihood functions. Journal of American Statistical Association, 90, 141-150.
16. Fan, J., Huang, T. and Li, R. (2005). Analysis of longitudinal data with semiparametric estimation of covariance function. Manuscript.
17. Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of American Statistical Association, 96, 1348-1360.
18. Fan, J and Li, R. (2004). New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis, Journal of American Statistical Association, 99, 710-72.
19. Fan, J. and Zhang, J. (2000). Two-step estimation of functional linear models with applications to longitudinal data. Journal of Royal Statistical Society, Series B, 62, 303-322.
20. Fan, J., Yao, Q., and Cai, Z. (2003). Adaptive varying-coefficient linear models, Journal of Royal Statistical Society, Series B, 65, 57-80.
21. Faraway, J. J. (1997). Regression analysis for a functional response. Technometrics, 39, 254-261.
22. Faraway, J.J. (1999). A graphical method of exploring the mean structure in longitudinal data analysis. Journal of Computational and Graphical Statistics, 8, 60-68.
23. Fung, W. K., Zhu, Z. Y., Wei, B. C. and He, X. (2002). Influence diagnostics and outlier tests for semiparametric mixed models. Journal of Royal Statistical Society, Series B, 64 565-579.
24. Härdle, W. Liang, H. and Gao, J. (1999). Partially Linear Models, Springer- Verlag, New York.
25. Hart, J.D. (1991). Kernel regression estiamtion with time-series errors. Journal of Royal Statistical Society, Series B, 53, 173-187.
26. Hart, J. D. and Wehrly, T. E. (1986). Kernel regression estimation using repeated measurements data. Journal of American Statistical Association, 81, 1080-1088.
27. Hastie, T. and Tibshirani, R. J. (1993). Varying-coefRcient models (with discussion). Journal of Royal Statistical Society, Series B, 55, 757-796.
28. He, X., Zhu, Z. Y., and Fung, W. K. (2002). Estimation in a semiparametric model for longitudinal data with unspecified dependence structure. Biometrika, 89, 579-590.
29. Heckman, N. E. (1986). Spline smoothing in partly linear models, Journal of Royal Statistical Society, Series B, 48, 244-248.
30. 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.
31. Huang, J. Z., Liu, N. and Pourahmadi, M. (2005). Covariance selection and estimation via penalized normal likelihood. Biometrika. To appear.
32. 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.
33. Huang, J. Z, Wu, C.O. and Zhou, L. (2004). Polynomial spline estimation and inference for varying coefficient models with longitudinal data. Statistica Sinica, 14, 763-788.
34. Kaslow, R.A., Ostrow, D.G., Detels, R. Phair, J.P., Polk, B.F. and Rinaldo, C.R. (1987). The Multicenter AIDS Cohort Study: rationale, organization and selected characteristics of the participants. Am. J. Epidem., 126, 310-318.
35. Kauermann G. (2000). Modeling longitudinal data with ordinal response by varying coefficients, Biometrics, 56, 692-698.
36. Li, R., Root, T. and Shiffman, S. (2005). A local linear estimation procedure for functional multilevel modeling. In Models for Intensively Longitudinal Data, (T. Walls and J. Schafer eds), 63-83. Oxford University Press.
37. Liang, H., Wang, S.J., Robins, J.M. and Carroll, R.J. (2004). Estimation in partially linear models with missing covariates Journal of American Statistical Association, 99, 357-367.
38. Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22
39. Lin, D.Y. and Ying, Z. (2001). Semiparametric and nonparametric regression analysis of longitudinal data (with discussion). Journal of American Statistical Association, 96, 103-126.
40. Lin, X. and Carroll, R. J. (2000). Nonparametric function estimation for clustered data when the predictor is measured without/with error. Journal of American Statistical Association, 95, 520-534.
41. Lin, X. and Carroll, R.J. (2001a). Semiparametric regression for clustered data. Biometrika, 88, 1179-1185.
42. Lin, X, and Carroll, R.J. (2001b). Semiparametric regression for clustered data using generalized estimating equations. Journal of American Statistical Association, 96, 1045-1056.
43. Lin, X., Wang, N. Y., Welsh, A. H, and Carroll, R.J. (2004). Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data. Biometrika, 91, 177-193.
44. Lin, X. and Zhang, D. (1999) Inference in generalized additive mixed models by using smoothing splines. Journal of Royal Statistical Society, Series B, 61, 381-400.
45. Martinussen, T. and Scheike, T.H. (1999). A semiparametric additive regression model for longitudinal data. Biometrika, 86, 691-702.
46. Moyeed, R.A. and Diggle, P.J. (1994). Rates of convergence in semiparametric modeling of longitudinal data. Austr. Jour. Statist., 36, 75-93.
47. Müller, H. G. (1988). Nonparametric Regression Analysis of Longitudinal Data. Springer-Verlag, New York.
48. Pourahmadi, M. (1999). Joint mean-covariance models with applications to longitudinal data: unconstrained parameterization. Biometrika, 86, 677-690.
49. Pourahmadi, M. (2000). Maximum likelihood estimation of generalized linear models for multivariate normal covariance matrix. Biometrika, 87, 425- 435.
50. Peterson, D.R., Zhao, H. and Eapen, S. (2003). Using local correlation in kernel- based smoothers for dependent data. Biometrics, 59, 984-991.
51. Qu, A. and Li, R. (2005). Quadratic inference functions for varying coefficient models with longitudinal data, Biometrics. To appear.
52. Qu, A., Lindsay, B. G., and Li, B. (2000). Improving generalised estimating equations using quadratic inference functions. Biometrika, 87, 823-836.
53. Rice, J. A. and Wu, C. O. (2003). Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics, 57, 253-259.
54. Ross, S. M. (1997). Simulation. Second Edition. Academic Press, Inc., San Diego, CA.
55. Ruckstuhl, A.,Welsh, A. H. and Carroll, R.J. (2000). Nonparametric function estimation of the relationship between two repeatedly measured variables. Statistica Sinica, 10, 51-71.
56. Ruppert, D., Sheather, S.J. and Wand, M.P. (1995). An effective bandwidth selector for local least squares regression. Journal of American Statistical Association, 90, 1257-1270.
57. Severini, T.A. and Staniswalis, J.G. (1994). Quasi-likelihood estimation in semiparametric models. Journal of American Statistical Association, 89, 501-511.
58. Silverman, B. W. (1984). Spline smoothing: the equivalent variable kernel method. Annals of Statistics, 12, 501-511.
59. Speckman, P. (1988). Kernel smoothing in partial linear models. Journal of Royal Statistical Society, Series B, 50, 413-436.
60. Sun, Y. and Wu, H. (2005). Semiparametric time-varying coefficients regression model for longitudinal data. Scandinavian Journal of Statistics, 32, 21 -47.
61. Tibshirani, R. J. (1996). Regression shrinkage and selection via the LASSO. Journal of Royal Statistical Society, Series B, 58, 267-288.
62. Wahba, G. (1984). Partial spline models for semiparametric estimation of functions of several variables, in Statist. Analysis of Time Ser., Proceedings of the Japan U.S. Joint Seminar, Tokyo, 319-329.
63. Wang, N. (2003). Marginal nonparametric kernel regression accounting for within- subject correlation. Biometrika, 90, 43-52.
64. Wang, N., Carroll, R. J. and Lin, X. (2005). Efficient semiparametric marginal estimation for longitudinal/clustered data. Journal of American Statistical Association, 100, 147-157.
65. Welsh, A. H., Lin, X. and Carroll, R.J. (2002). Marginal longitudinal nonparametric regression: Locality and efficiency of spline and kernel methods. Journal of American Statistical Association, 97, 482-493.
66. Wu, C. O. and Chiang, C.-T. (2000). Kernel smoothing on varying coefficient models with longitudinal dependent variable. Statistica Sinica, 10, 433- 456.
67. 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. Journal of American Statistical Association, 93, 1388-1402.
68. Wu, H. and Liang, H. (2004). Random Varying-Coefficient Models with Smoothing Covariates, Applications to an AIDS Clinical Study. Scan. J. Statist., 31, 3-19.
69. Wu, F. and Zhang, J. (2002). Local polynomial mixed-efiects models for longitudinal data. Journal of American Statistical Association, 97, 883-897.
70. Wu, W. B. and Pourahmadi, M. (2003). Nonparametric estimation of large covariance matrices of longitudinal data. Biometrika, 90, 831-844.
71. Xiao, Z., Linton, O.B., Carroll, R.J, and Mammen, E. (2003). More efficient local polynomial estimation in nonparametric regression with autocorrelated errors. Journal of American Statistical Association, 98, 980-992.
72. Yao, F., Müller, H.G. and Wang, J.-L. (2005a). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association, 100, 577-590.
73. Yao, F., Müller, H.G., Wang, J. L. (2005b). Functional Regression Analysis for Longitudinal Data. The Annals of Statistics, in press.
74. 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.
75. Zhang, D. (2004). Generalized linear mixed models with varying coefficients for longitudinal data. Biometrics, 60, 8-15.
76. Zhang, D. and Davidian, M. (2004). Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data. Journal of Multivariate Analysis, 91, 90-106.
77. Zhang, D. and Lin, X. (2003). Hypothesis testing in semiparametric additive mixed models. Biostatistics, 4, 57-74.
78. Zhang, D., Lin, X., Raz, J., and Sowers, M. F. (1998). Semiparametric stochastic mixed models for longitudinal data. Journal of American Statistical Association, 93, 710-719.
79. Zhang, D., Lin, X. and Sowers, M.F. (2000). Semiparametric regression for periodic longitudinal hormone data from multiple menstrual cycles. Biometrics, 56, 31-39.