Discrimination de courbes par régression inverse fonctionnelle
Revue de Statistique Appliquée, Volume 53 (2005) no. 1, p. 39-57
@article{RSA_2005__53_1_39_0,
     author = {Ferr\'e, Louis and Villa, Nathalie},
     title = {Discrimination de courbes par r\'egression inverse fonctionnelle},
     journal = {Revue de Statistique Appliqu\'ee},
     publisher = {Soci\'et\'e fran\c caise de statistique},
     volume = {53},
     number = {1},
     year = {2005},
     pages = {39-57},
     language = {fr},
     url = {http://www.numdam.org/item/RSA_2005__53_1_39_0}
}
Ferré, Louis; Villa, Nathalie. Discrimination de courbes par régression inverse fonctionnelle. Revue de Statistique Appliquée, Volume 53 (2005) no. 1, pp. 39-57. http://www.numdam.org/item/RSA_2005__53_1_39_0/

[1] Bosq D. ( 1991), Modelization, non-parametric estimation and prediction for continuous time processes. In : Roussas, G. (Ed. ), Nonparametric Functional estimation and related Topics, NATO, ASI Series, pp. 509-529. | MR 1154349 | Zbl 0737.62032

[2] Cook R.D. ( 1991), Discussion of Li (1991) J. Am. Statis. Ass., 86, 328-332.

[3] Cook R.D.et Yin X. ( 2001), Dimension reduction and visualization in discriminant analysis, Australian & New-Zealand Journal of Statistics, 43, 147-199. | MR 1839361 | Zbl 0992.62056

[4] Dauxois J., Ferré L. and Yao A.F. ( 2001), Un modèle semi-paramétrique pour variable aléatoire Hilbertienne. C.R. Acad. Sci. Paris, t.327, série I, 947-952. | MR 1873814 | Zbl 0996.62035

[5] Dauxois J. and Pousse A. ( 1976), Les analyses factorielles en calcul des probabilités et en statistique : essai d'étude synthétique. Thèse Toulouse III.

[6] Devroye L., Györfi L. and Lugosi G. ( 1996), A probabilistic theory for pattern recognition, New-York : Springer-Verlag. | MR 1383093

[7] Dipillo P. ( 1979), Biased discriminant analysis : evaluation of the optimum probability of classification, Comm. Statist. Theory Methods, 8, 1447-1458. | MR 547408 | Zbl 0414.62045

[8] Ferraty F. and Vieu P. ( 2003), Curves Discrimination : a Non Parametric Approach. Computational and Statistical Data Analysis, 44, 161-173. | MR 2020144 | Zbl pre05373903

[9] Ferré L. and Villa N. ( 2005), Multi-layer Neural Network with Functional Inputs, soumis à publication.

[10] Ferré L. and Yao A. F. ( 2003), Functional Sliced Inverse Regression analysis. Statistics, 37, 475-488. | MR 2022235 | Zbl 1032.62052

[11] Ferré L. et Yao A.F. ( 2005), Smoothed Functional Inverse Regression. À paraître dans Statistica Sinica. | MR 2233905 | Zbl 1086.62054

[12] Friedman J. ( 1989), Regularized discriminant analysis, J. Amer. Statist. Assoc., 84, 165-175. | MR 999675

[13] Hand D.J. ( 1982), Kernel discriminant analysis, Research Studies Press/Wiley. | MR 666869 | Zbl 0562.62041

[14] Hastie T., Tibshirani R. and Buja A. ( 1994), Flexible Discriminant Analysis by optimal scoring, J. Amer. Statist. Ass., 89, 1255-1270. | MR 1310220 | Zbl 0812.62067

[15] Hastie T., Buja A. and Tibshirani R. ( 1995), Penalized Discriminant Analysis, Ann. Statist., 23, p 73-102. | MR 1331657 | Zbl 0821.62031

[16] Hernandez A. et Velilla S. ( 2001), Dimension reduction in nonparametric discriminant analysis, Technical report.

[ 17] Hoerl A.E. and Kennard R.W. ( 1970a), Ridge regression :biased estimation for non orthogonal problems, Technometrics, 12-1, 55-67. | MR 370945 | Zbl 0202.17205

[18] Hoerl A.E. and Kennard R.W. ( 1970b), Ridge regression : Application to non orthogonal problems, Technometrics, 12-2, 69-82. | Zbl 0202.17206

[19] Hsing T. ( 1999), Nearest Neighbor Inverse Regression, Ann. Statist., 697-731. | MR 1714711 | Zbl 0951.62034

[20] James G.M. and Hastie T.J. ( 2001), Functional linear discriminant analysis for irregularly sampled curves, J.R. Statis. Soc., B, 64, 533-550. | MR 1858401 | Zbl 0989.62036

[21] Leurgans S.E., Moyeed R.A. and Silverman B.W. ( 1993), Canonical Correlation Analysis when the data are curves, J.R. Statis. Soc., B, 55,725-740. | MR 1223939 | Zbl 0803.62049

[22] Li K. C. ( 1991), Sliced Inverse Regression for dimension reduction, J. Amer. Statist. Ass., 86, 316-342. | MR 1137117 | Zbl 0742.62044

[23] Li K. C. ( 1992), On principal Hessian directions for data visualisation and dimension reduction : another application of Stein's lemma, Ann. Statist., 87, 1025-1039. | MR 1209564 | Zbl 0765.62003

[24] Li K.C., Aragon Y., Shedden K et Thomas-Agan C. ( 2003), Dimension reduction for multivariate data, J. Amer. Statist. Ass., 98, 99-109. | MR 1965677 | Zbl 1047.62059

[25] Ramsay J. O. and Silverman B. W. ( 1997), Functional Data Analysis, New-York : Springer Verlag. | MR 2168993 | Zbl 0882.62002