Varying-coefficient models and basis function approximations for the analysis of repeated measurements

Biometrika

Volumn 89, Issue 1, 2002, Pages 111-128

  Huang, Jianhua Z ^a   Wu, Colin O ^b   Zhou, Lan ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Basis function; Confidence band; Hypothesis testing; Least squares; Longitudinal data; Polynomial spline; Resampling subject bootstrap; Varying coefficient model

Indexed keywords

EID: 0011799801     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/89.1.111     Document Type: Article

References (25)

1. BOOR, C. DE (1978). A Practical Guide to Splines. New York: Springer.
2. CHIANG, C. T., RICE, J. A. & WU, C. O. (2001). Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. J. Am. Statist. Assoc. 96, 605-19.
3. DAVIDIAN, M. & GILTINAN, D. M. (1995). Nonlinear Models for Repeated Measurement Data. London: Chapman and Hall.
4. DIGGLE, P. J., LIANG, K.-Y. & ZEGER, S. L. (1994). Analysis of Longitudinal Data. Oxford: Oxford University Press.
5. FAN, J. & ZHANG, J.-T. (2000). Functional linear models for longitudinal data. J. R. Statist. Soc. B 62, 303-22.
6. HALL, P. & TITTERINGTON, D. M. (1988). On confidence bands in nonparametric density estimation and regression. J. Mult. Anal. 27, 228-54.
7. HART, J. D. (1997). Nonparametric Smoothing and Lack-of-Fit Tests. New York: Springer-Verlag.
8. HART, J. D. & WEHRLY, T. E. (1986). Kernel regression estimation using repeated measurements data. J. Am. Statist. Assoc. 81, 1080-8.
9. HART, J. D. & WEHRLY, T. E. (1993). Consistency of cross-validation when the data are curves. Stoch. Proces. Appl. 45, 351-61.
10. HASTIE, T. J. & TIBSHIRANI, R. J. (1993). Varying-coefficient models. J. R. Statist. Soc. B 55, 757-76.
11. HOOVER, D. R., RICE, J. A., WU, C. O. & YANG, L.-P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85, 809-22.
12. HUANG, J. Z. (1998). Projection estimation in multiple regression with applications to functional ANOVA models. Ann. Statist. 26, 242-72.
13. KASLOW, R. A., OSTROW, D. G., DETELS, R., PHAIR, J. P., POLK, B. F. & RINALDO, C. R. (1987). The Multicenter AIDS Cohort Study: rationale, organization and selected characteristics of the participants. Am. J. Epidem. 126, 310-8.
14. LIN, X. & CARROLL, R. J. (2000). Nonparametric function estimation for clustered data when the predictor is measured without/with error. J. Am. Statist. Assoc. 95, 520-34.
15. MOYEED, R. A. & DIGGLE, P. J. (1994). Rates of convergence in semiparametric modelling of longitudinal data. Aust. J. Statist. 36, 75-93.
16. MÜLLER, H.-G. (1988). Nonparametric Regression Analysis of Longitudinal Data, Lecture Notes in Statistics, 46. Berlin: Springer-Verlag.
17. NAIMAN, D. & WYNN, H. (1997). Abstract tubes, improved inclusion-exclusion identities and inequalities and importance sampling. Ann. Statist. 36, 75-93.
18. RAMSAY, J. O. & SILVERMAN, B. W. (1997). Functional Data Analysis. New York: Springer-Verlag.
19. 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.
20. RICE, J. A. & WU, C. O. (2001). Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics 57, 253-9.
21. SCHUMAKER, L. (1981). Spline Functions: Basic Theory. New York: John Wiley & Sons.
22. STONE, C. J. (1982). Optimal global rates of convergence for nonparametric regression. Ann. Statist. 10, 1348-60.
23. VONESH, E. F. & CHINCHILLI, V. M. (1997). Linear and Nonlinear Models for the Analysis of Repeated Measurements. New York: Marcel Dekker.
24. WU, C. O. & CHIANG, C.-T. (2000). Kernel smoothing on varying coefficient models with longitudinal dependent variable. Statist. Sinica 10, 433-56.
25. 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.