Abstract
After a review of the mainly dimensionality reduction methods as well as of the Shrinkage Regression Methods, authors provide a different multivariate extension of the univariate PLS (1994) highlighting a different use and interpretation.
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ABRAHAM, B. and MEROLA, G. (2001): Dimensionality reduction approach to multivariate prediction. In: Esposito Vinzi V. et al (Eds.): PLS and related methods, CISIA ceresta.
BJÖRKSTRÖM, A. and SUNDBERG, R. (1996): Continuum regression is not always continuous. Journal of the Royal Statistical Society, Series B, 58:4, 703–710.
BJÖRKSTRÖM, A. and SUNDBERG, R. (1999): A generalized view on continuum regression. Scandinavian Journal of Statistics, 26:1, 17–30.
BROOKS, R. and STONE, M. (1994): Joint continuum regression for multiple predictands. JASA, 89, 1374–1377.
BROWN P.J. (1993): Measurement, Regression and Calibration. Oxford Univ. Press, Oxford.
CHESSEL, D. and HANAFI, M. (1996): Analyse de la co-inertie de K nuages de points. RSA, XLIV, 35–60.
D’AMBRA, L. and LAURO, N.C. (1982): Analisi in componenti principali in rapporto ad un sottospazio di riferimento. Rivista di Statistica Applicata, n. 1, vol.15.
D’AMBRA, L., SABATIER, R. and AMENTA, P. (1998): Analisi fattoriale delle matrici a tre vie: sintesi e nuovi approcci. Italian Journal of Applied Statistics, vol.13, n.2, (2002).
DE JONG, S. and KIERS, H.A.L. (1992): Principal covariates regression. Part 1. Theory, Chemometrics and Intelligent Laboratory Systems, 14, 155–164.
FRANK, I.R. and FRIEDMAN, J.H. (1993): A statistical view of some chemometrics regression tools. Technometrics, 35, 109–148.
GARTHWAITE, P.H. (1994): An interpretation of partial least squares. JASA, 89.
HOERL, A.E. (1962): Application of ridge analysis to regression problems. Chemical Engineering Progress, 58, 54–59.
HOERL, A.E. and KENNARD, R.W. (1970): Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12, 55–67.
HSÖKULDSSON, A. (1992): The H-principle in modelling with applications to chemometrics. Chemometrics and Intelligent Laboratory Systems, 14, 139–153.
STONE, M. and BROOKS, R.J. (1990): Continuum regression: cross validated sequentially constructed prediction embracing ordinary least squares and principal component regression. J. Royal Stat. Soc., B, 2.
SUNDBERG, R. (1993): Continuum regression and ridge regression. J. R. Statist. Soc., B 55, 653–659.
WOLD, H. (1966): Estimation of principal components and related models by iterative least squares, In: Krishnaiah P. R. (Ed.): Multivariate Analysis, Ac. Press, New York.
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D’Ambra, L., Amenta, P., Lombardo, R. (2003). A Dimensionality Reduction Method Based on Simple Linear Regressions. In: Schader, M., Gaul, W., Vichi, M. (eds) Between Data Science and Applied Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18991-3_23
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DOI: https://doi.org/10.1007/978-3-642-18991-3_23
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