Quantile regression when the covariates are functions

Journal of Nonparametric Statistics

Volumn 17, Issue 7, 2005, Pages 841-856

  Cardot, Hervé ^a   Crambes, Christophe ^b   Sarda, Pascal ^c  

^a CEMAGREF   (France)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^c UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

spline functions; Conditional quantiles; Functional data analysis; Roughness penalty

Indexed keywords

EID: 27744593604     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485250500303015     Document Type: Article

References (27)

1. Ramsay, J.O. and Silverman, B.W., 2002, Applied Functional Data Analysis (Springer-Verlag).
2. Deville, J.C., 1974, Methodes Statistiques et Numériques de l'Analyse Harmonique (in French), Ann. Insee, 15.
3. Dauxois, J. and Pousse, A., 1976, Les Analyses Factorielles en Calcul des Probabilités et en Statistique: Essai d'étude synthétique (in French). Thèse, Université Paul sabatier, Toulouse, France.
4. Besse, P.C. and Ramsay, J.O., 1986, Principal component analysis of sampled curves. Psychometrika, 51, 285-311.
5. Ramsay, J.O. and Silverman, B.W., 1997, Functional Data Analysis (Springer-Verlag).
6. Ferraty, F. and Vieu, P., 2002, The functional nonparametric model and application to spectrometric data. Computational Statistics, 17, 545-564.
7. Koenker, R.W. and Bassett G.W., 1978, Regression quantiles. Econometrica, 46, 33-50.
8. Bassett, G. W. and Koenker, R.W., 1978, Asymptotic theory of least absolute error regression. Journal of the American Statistical Association, 73, 618-622.
9. Bhattacharya, P.K. and Gangopadhyay, A.K., 1990, Kernel and nearest-neighbor estimation of a conditional quantile. Annals of Statistics, 18, 1400-1415.
10. Tsybakov, A.B., 1986, Robust reconstruction of functions by the local approximation method. Problems of Information Transmission, 22, 133-146.
11. Lejeune, M. and Sarda, P., 1988, Quantile regression: a nonparametric approach. Computational Statistics and Data Analysis, 6, 229-239.
12. Fan, J., Hu, T.C. and Truong, Y.K., 1994, Robust nonparametric function estimation. Scandinavian Journal of Statistics, 21, 433-446.
13. He, X. and Shi, P., 1994, Convergence rate of B-Spline estimators of nonparametric conditional quantile functions. Nonparametric Statistics, 3, 299-308.
14. Koenker, R.W., Ng, P. and Portnoy, S., 1994, Quantile smoothing splines. Biometrika, 81, 673-680.
15. de Boor, C., 1978, A Practical Guide to Splines (New-York: Springer).
16. 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.
17. Weinberger, H.F., 1974, Variational Methods for Eigenvalue Approximation (Philadelphia: SIAM).
18. Cardot, H., Ferraty, F. and Sarda, P., 2003, Spline estimators for the functional linear model. Statistica Sinica, 13, 571-591.
19. Bosq, D., 2000, Linear Processes in Function Spaces. Lecture Notes in Statistics, Vol. 149 (Springer-Verlag).
20. Stone, C., 1982, Optimal rates of convergence for nonparametric models. Annals of Statistics, 10, 1040-1053.
21. Ruppert, D. and Carroll, R.J., 1988, Transformation and Weighting in Regression (Chapman and Hall).
22. Cardot, H., Crambes, C. and Sarda, P., 2004, Conditional quantiles with functional covariates: an application to ozone pollution forecasting. In: J. Antoch (Ed.) Compstat 2004 Proceedings (Physica-Verlag), pp. 769-776.
23. Stone, C., 1985, Additive regression and other nonparametric models. Annals of Statistics, 13, 689-705.
24. Uspensky, J.V., 1937, Introduction to Mathematical Probability (New York and London: McGraw Hill Book Company).
25. Cardot, H., Ferraty, F. and Sarda, P., 1999, The functional linear model. Statistic and Probability Letters, 45, 11-22.
26. Frank, I.E. and Friedman, J.H., 1993, A statistical view of some chemometrics regression tools (with discussion). Technometrics, 35, 109-148.
27. Ramsay, J.O. and Dalzell, C.J., 1991, Some tools for functional data analysis. Journal of the Royal Statistical Society Series B, 3, 539-572.