Nonparametric estimation of smoothed principal components analysis of sampled noisy functions

Journal of Nonparametric Statistics

Volumn 12, Issue 4, 2000, Pages 503-538

  Cardot, Hervé ^a  

^a CEMAGREF   (France)

Author keywords

Asymptotic expansion; B splines; Functional principal component analysis; Hybrid splines; Mean square error; Nonparametric regression; Rates of convergence

Indexed keywords

EID: 0001469917     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485250008832820     Document Type: Article

References (23)

1. Agarwal, G. and Studden, W. (1980) Asymptotic integrated mean square error using least squares and bias minimizing splines. The Annals of Statistics, 8, 1307-1325.
2. Besse, P. (1991) Approximation spline de l'analyse en composantes principales d'une variable aléatoire hilbertienne. Annales de la Faculté des sciences de Toulouse, 12, 329-346.
3. Besse, P., Cardot, H. and Ferraty, F. (1997) Simultaneous nonparametric regressions of unbalanced longitudinal data. Computational Statistics and Data Analysis, 24, 255-270.
4. Biritxinaga, E. (1987) Estimation spline de la moyenne d'une fonction aléatoire. Thèse de troisième cycle, Université de Pau, France.
5. Bosq, D. (1991) Modelization, nonparametric estimation and prediction for continuous time processes. In: Roussas, G., Editor, Nonparametric Functional Estimation and Related Topics, pp. 509-529, Nato, Asi Series.
6. Boularan, J., Ferré, L. and Vieu, P. (1993) Growth curves: a two stage nonparametric approach. Journal of Statistical Planning and Inference, 38, 327-350.
7. Burman, P. (1991) Regression function estimation from dependant observations. Journal of Multivariate Analysis, 36, 263-279.
8. Cardot, H. (1997) Contribution à l'estimation et à la prévision statistique de données fonctionnelles. Thèse de troisième cycle, Université Paul Sabatier, Toulouse, France.
9. Cardot, H. and Diack, C. (1998) Convergence en moyenne quadratique de l'estimateur de la régression par splines hybrides. C.R. Acad. Sci. Paris, Série I, t.326, 615-618.
10. Chatelin, F. (1983) Spectral Approximation of Linear Operators. Academic Press.
11. Dauxois, J., Pousse, A. and Romain, Y. (1982) Asymptotic theory for the principal component analysis of a random vector function: Some applications to statistical inference. Journal of Multivariate Analysis, 12, 136-154.
12. Diack, C. and Thomas-Agnan, C. (1997) A nonparametric test of non-convexity of the regression. To appear in Journal of Nonparametric Statistics.
13. De Boor, C. (1978) A practical Guide to Splines. Springer Verlag.
14. Hart, J. and Wehrly, T. (1993) Consistency of cross-validation when data are curves. Stochastic processes and their Applications, 45, 351-361.
15. Kato, T. (1976) Perturbation Theory of Linear Operator. Springer-Verlag.
16. Kelly, C. and Rice, J. (1990) Monotone smoothing with application to dose-response curves and the assessment of synergism. Biometrics, 46, 1071-1085.
17. Kneip, A. (1995) Nonparametric estimation of common regressors for similar curve data. The Annals of Statistics, 22, 1386-1427.
18. Pezzulli, S. and Silverman, B. (1993) On smoothed principal components analysis. Computational Statistics, 8, 1-16.
19. Ramsay, J. and Dalzell, C. (1991) Some tools for functional data analysis. Journal of the Royal Statistical Society, B, 53, 539-572. with discussion.
20. Ramsay, J. and Silverman, B. (1997) Functional Data Analysis. Springer-Verlag.
21. Rice, J. and Silverman, B. (1991) Estimating the mean and covariance nonparametrically when the data are curves. Journal of the Royal Statistical Society, B, 53, 233-243.
22. Schumaker, L. (1981) Spline Functions: Basic Theory. Wiley-Interscience.
23. Silverman, B. (1996) Smoothed functional principal components analysis by choice of norm. The Annals of Statistics, 24, 1-24.