Cross-validated estimations in the single-functional index model

Statistics

Volumn 42, Issue 6, 2008, Pages 475-494

  Ait Saïdi, Ahmed ^a   Ferraty, Frédéric ^b   Kassa, Rabah ^a   Vieu, Philippe ^b  

^a UNIVERSITY OF BEJAIA   (Algeria)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Adaptative semi metric; Cross validation; Data driven selection of functional index; Functional data analysis; Functional index model; Mean integrated squared error; Nonparametric statistics; Optimality properties

Indexed keywords

EID: 54349129142     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331880801980377     Document Type: Article

References (28)

1. W. Härdle, P. Hall, and H. Ichumira, Optimal smoothing in single-index models, Ann. Statist. 21 (1993), pp. 157-178.
2. J. Horowitz and W. Härdle, Direct semiparametric estimation of single-index models, J. Amer. Statist. Assoc. 91 (1996), pp. 1632-1640.
3. R.J. Caroll et al., Generalized partially linear single-index models, J. Amer. Statist. Assoc. 92 (1997), pp. 477-489.
4. M. Delecroix and M. Hristache, M-estimateurs semi-paramétriques dans les modèles à direction révélatrice unique, Bull. Belg. Math. Soc. Simon Stevin 6 (1999), pp. 161-185.
5. Y. Xia, H. Tong, and W.K. Li, On extended partially linear single-index models, Biometrika 86 (1999), pp. 363-410.
6. M. Hristache, A. Juditsky, and V. Spokoiny, Direct estimation of the index coefficient in the single-index model, Ann. Statist. 29 (2001), pp. 595-623.
7. Y. Xia et al., An adaptative estimation of dimension reduction space, J. R. Statist. Soc. B 64 (2002), pp. 363-410.
8. F. Ferraty and P. Vieu, Non Parametric Functional Data Analysis: Theory and Practice, Springer Series in Statistics, Springer, New York, 2006.
9. F. Ferraty and P. Vieu, The functional nonparametric model and application to spectrometric data, Comput. Statist. 17 (2002), pp. 545-564.
10. S. Dabo-Niang, F. Ferraty, and P. Vieu, Mode estimation for functional random variable and its application for curves classification, Far East J. Theor. Stat. 18 (2006), pp. 93-119.
11. S. Dabo-Niang, F. Ferraty, and P. Vieu, On the using of modal curves for radar waveforms classification, Comp. Statist. Data Anal. 51 (2007), pp. 4878-4890.
12. P. Hall, P. Poskitt, and P. Presnell, A functional data-analytic approach to signal discrimination, Technometrics 43 (2001), pp. 1-9.
13. F. Ferraty, A. Rabhi, and P. Vieu, Conditional quantiles for dependent functional data with application to the climatic El Niño phenomenon, Sankhya 67 (2005), pp. 378-398.
14. J. Ramsay and B.W. Silverman, Functional Data Analysis, Springer-Verlag, New York, 1997.
15. J. Ramsay and B.W. Silverman, Applied Functional Data Analysis: Methods and Case Studies, Springer-Verlag, New York, 2002.
16. F. Ferraty, A. Peuch, and P. Vieu, Modèle à indice fonctionnel simple, C.R. Acad. Sci. Paris Ser. I 336 (2003), pp. 1025-1028.
17. A. Ait Saidi, F. Ferraty, and R. Kassa, Single functional index model for a time series, Rev. Roumaine Math. Pures Appl. 50 (2005), pp. 321-330.
18. T. Hastie and C. Mallows, Discussion, Technometrics 35 (1993), pp. 140-143.
19. H. Cardot, F. Ferraty, and P. Sarda, Functional linear model, Statist. Prob. Lett. 45 (1999), pp. 11-22.
20. H. Cardot, F. Ferraty, and P. Sarda, Spline estimators for the functional linear model, Statist. Sinica 13 (2003), pp. 571-591.
21. A. Cuevas, M. Febrero, and R. Fraiman, Linear function regression: The case of fixed design and functional response, Canad. J. Statist. 30 (2002), pp. 285-300.
22. W. Härdle and J.S. Marron, Optimal bandwidth selection in nonparametric regression function estimation, Ann. Statist. 13 (1985), pp. 1465-1481.
23. J.S. Marron, A comparison of cross-validation techniques in density estimation, Ann. Statist. 15 (1987), pp. 152-162.
24. P. Sarda and P. Vieu, Smoothing parameter selection in hazard estimation, Statist. Proba. Let. 11 (1991), pp. 429-434.
25. F. Ferraty, A. Mas, and P. Vieu, Nonparametric regression on functional data: Inference and prectical aspects, Aust. N. Z. J. Stat. 49 (2007), pp. 267-286.
26. R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2006. Available at http://www.R-project.org.
27. F. Ferraty and P. Vieu, Nonparametric models for functional data, with applications in regression, time series prediction and curves discrimination, J. Nonparametr. Statist. 16 (2004), pp. 11-127.
28. J.S. Marron and W. Härdle, Random approximations to some measures of accuracy in nonparametric curve estimation, J. Multivar. Anal. 20 (1986), pp. 91-113.