Penalized spline models for functional principal component analysis

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 68, Issue 1, 2006, Pages 3-25

  Yao, Fang ^a   Lee, Thomas C M ^a  

^a Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

Asymptotics; Functional data; Penalized spline regression; Principal components; Smoothing; Within subject correlation

Indexed keywords

EID: 33645031408     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2005.00530.x     Document Type: Article

References (29)

1. Berkey, C. S., Laird, N. M., Valadian, I. and Gardner, J. (1991) Modelling adolescent blood pressure patterns and their prediction of adult pressures. Biometrics, 47, 1005-1018.
2. Besse, P. and Ramsay, J. O. (1986) Principal components analysis of sampled functions. Psychometrika, 51, 285-311.
3. Bhattacharya, P. K. and Müller, H. G. (1993) Asymptotics for nonparametric regression. Sankhya A, 55,420-441.
4. Boente, G. and Fraiman, R. (2000) Kernel-based functional principal components. Statist. Probab. Lett., 48, 335-345.
5. Brumback, B. and Rice, J. A. (1998) Smoothing spline models for the analysis of nested and crossed samples of curves (with discussion). J. Am. Statist. Ass., 93, 961-1006.
6. Burnham, K. P. and Anderson, D. R. (2002) Model Selection and Inference: a Practical Information-theoretic Approach, 2nd edn. New York: Springer.
7. Castro, P. E., Lawton, W. H. and Sylvestre, E. A. (1986) Principal modes of variation for processes with continuous sample curves. Technometrics, 28, 329-337.
8. Chiou, J.-M., Müller, H. G. and Wang, J.-L. (2003) Functional quasi-likelihood regression models with smooth random effects. J. R. Statist. Soc. B, 65, 405-423.
9. Fan, J. and Zhang, J.-T. (2000) Two-step estimation of functional linear models with applications to longitudinal data. J. R. Statist. Soc. B, 62, 303-322.
10. Hall, P. and Opsomer, J. D. (2005) Theory for penalised spline regression, Biometrika, 92, 105-118.
11. James, G., Hastie, T. G. and Sugar, C. A. (2001) Principal component models for sparse functional data. Biometrika, 87, 587-602.
12. Jones, M. C. and Rice, J. (1992) Displaying the important features of large collections of similar curves. Am. Statistn, 46, 140-145.
13. Lin, X. and Carroll, R. J. (2000) Nonparametric function estimation for clustered data when the predictor is measured without/with error. J. Am. Statist. Ass., 95, 520-534.
14. Lin, X., Wang, N., Welsh, A. H. and Carroll, R. J. (2004) Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data. Biometrika, 91, 177-193.
15. O'Sullivan, F. (1986) A statistical perspective on ill-posed inverse problems. Statist. Sci., 1, 502-518.
16. Ramsay, J. and Silverman, B. (1997) Functional Data Analysis. New York: Springer.
17. Rao, C. R. (1958) Some statistical methods for comparison of growth curves. Biometrics, 14, 1-17.
18. Rice, J. A. and Silverman, B. W. (1991) Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Statist. Soc. B, 53, 233-243.
19. Rice, J. and Wu, C. (2000) Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics, 57, 253-259.
20. Ruppert, D. (2002) Selecting the number of knots for penalized splines. J. Computnl Graph. Statist., 11, 735-757.
21. Ruppert, D., Wand, M. P. and Carroll, R. J. (2003) Semiparametric Regression. Cambridge: Cambridge University Press.
22. Shi, M., Weiss, R. E. and Taylor, J. M. G. (1996) An analysis of paediatric CD4 counts for acquired immune deficiency syndrome using flexible random curves. Appl. Statist., 45, 151-163.
23. Silverman, B. (1996) Smoothed functional principal components analysis by choice of norm. Ann. Statist., 68, 45-54.
24. Spellman, P. T., Sherlock, G., Zhang, M. Q., Tyer, V. R., Eisen, M. B., Brown, P. O., Botstein, D. and Futcher, B. (1998) Comprehensive identification of cell cycle-regulated genes of the yeast saccharomyces cerevisiae by microarray hybridization. Molee. Biol. Cell, 9, 3273-3297.
25. Wang, N. (2003) Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika, 90, 43-52.
26. Wang, N., Carroll, R. J. and Lin, X. (2005) Efficient semiparametric marginal estimation for longitudinal/clustered data. J. Am. Statist. Ass., 100, 147-157.
27. Welsh, A. H., Lin, X. and Carroll, R. J. (2002) Marginal longitudinal nonparametric regression: locality and efficiency of spline and kernel methods. J. Am. Statist. Ass., 97, 482-493.
28. Yao, F., Müller, H. G., Clifford, A. J., Dueker, S. R., Follett, J., Lin, Y., Buchholz, B. A. and Vogel, J. S. (2003) Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate. Biometrics, 59, 676-685.
29. Yao, F., Müller, H. G. and Wang, J. L. (2005) Functional data analysis for sparse longitudinal data. J. Am. Statist. Ass., 100, 577-590.