Clusterwise PLS regression on a stochastic process. (English) Zbl 1429.62299

Summary: The clusterwise linear regression is studied when the set of predictor variables forms a \(L_{2}\)-continuous stochastic process. For each cluster the estimators of the regression coefficients are given by partial least square regression. The number of clusters is treated as unknown and the convergence of the clusterwise algorithm is discussed. The approach is compared with other methods via an application on stock-exchange data.


62J05 Linear regression; mixed models
62H25 Factor analysis and principal components; correspondence analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62P05 Applications of statistics to actuarial sciences and financial mathematics


fda (R)
Full Text: DOI HAL


[1] Aguilera, A.M.; Ocaña, F.; Valderama, M.J., An approximated principal component prediction model for continuous-time stochastic process, Appl. stochastic models data anal., 13, 61-72, (1997) · Zbl 0885.62109
[2] Bock, H.H., 1969. The equivalence of two extremal problems and its application to the iterative classification of multivariate data. Lecture Note, Vortragsausarbeitung, Tagung “Meolizinische Statistik”, Mathematisches Forschungsinstitut Oberwolfach, 1969, pp. 10.
[3] Cazes, P., Adaptation de la régression PLS au cas de la régression après analyse des correspondances multiples, Rev. statist. appl., XLIV, 4, 35-60, (1997)
[4] Charles, C., 1977. Régression typologique et reconnaissance des formes. Thèse de doctorat, Université Paris IX.
[5] de Jong, S., PLS fits closer than PCR, J. chemometr., 7, 551-557, (1993)
[6] DeSarbo, W.S.; Cron, W.L., A maximum likelihood methodology for clusterwise linear regression, J. classification, 5, 249-282, (1988) · Zbl 0692.62052
[7] Deville, J.C., Méthodes statistiques et numériques de l’analyse harmonique, Ann. l’INSEE France, 15, 3-101, (1974)
[8] Deville, J.C., Analyse et prévision des séries chronologiques multiples non stationnaires, Statist. anal. données, 3, 19-29, (1978)
[9] Escoufier, Y., Echantillonnage dans une population de variables aléatoires réelles, Publ. inst. statist. univ. Paris, 19, 4, 1-47, (1970) · Zbl 0264.62021
[10] Esposito Vinzi, V., Lauro, C., 2003. PLS regression and classification. PLS and Related Methods, Proceedings of the PLS’03 International Symposium, Decisia, Paris, pp. 45-56.
[11] Hennig, C., Models and methods for clusterwise linear regression, (), 179-187
[12] Hennig, C., Identifiability of models for clusterwise linear regression, J. classification, 17, 273-296, (2000) · Zbl 1017.62058
[13] Phatak, A., De Hoog, F., 2001. PLSR, Lanczos, and conjugate gradients. CSIRO Mathematical & Information Sciences, Report No. CMIS 01/122, Canberra.
[14] Plaia, A., 2001. On the number of clusters in clusterwise linear regression. Xth International Symposium on Applied Stochastic Models and Data Analysis, Proceedings, vol. 2, Compiegne, France, pp. 847-852.
[15] Preda, C., 1999. Analyse factorielle d’un processus: problèmes d’approximation et de régression, Thèse de doctorat, No. 2648. Université de Lille 1, France.
[16] Preda, C.; Saporta, G., Régression PLS sur un processus stochastique, Rev. statist. appl. (France), L, 2, 27-45, (2002)
[17] Ramsay, J.O.; Silverman, B.W., Functional data analysis, Springer series in statistics, (1997), Springer New York · Zbl 0882.62002
[18] Saporta, G., Méthodes exploratoires d’analyse de données temporelles. cahiers du B.U.R.O., no. 37-38, (1981), Université Pierre et Marie Curie Paris
[19] Spaeth, H., Clusterwise linear regression, Computing, 22, 367-373, (1979) · Zbl 0387.65028
[20] Tenenhaus, M., 1998. La régression PLS. Théorie et pratique, Editions Technip, Paris. · Zbl 0923.62058
[21] Wold, S.; Ruhe, A.; Dunn, W.J., The collinearity problem in linear regression. the partial least squares (PLS) approach to generalized inverses, SIAM J. sci. statist. comput., 5, 3, 735-743, (1984) · Zbl 0545.62044
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.