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Regression Splines for Multivariate Additive Modeling

  • Jean-François Durand
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Summary

Four additive spline extensions of some linear multiresponse regression methods are presented. Two of them are defined in this paper and their properties are compared with those of two other recently devised methods. Dimension reduction aspects and quality of the regression are discussed and illustrated on examples.

Keywords

Linear Discriminant Analysis Discriminant Variable Spline Coefficient Common Principal Component Generalize Principal Component Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bertier, P. and Bouroche, J.-M. (1975), Analyse des données multidimensionnelles, Paris: PUF. De Boor, C. (1978), A practical guide to splines, New York: Springer.Google Scholar
  2. Donnell, D. J. et al. (1994), Analysis of additive dependencies and concurvities using smallest ad-ditive principal components (with discussion), The Annals of Statistics, 4, 1635–1673.MathSciNetCrossRefGoogle Scholar
  3. Durand, J. F. (1992), Additive spline discriminant analysis, in Computationnal Statistics, Vol. 1, (Y. Dodge and J. Whittaker, eds. ), Physica-Verlag, 144–149.Google Scholar
  4. Durand, J. F. (1993), Generalized principal component analysis with respect to instrumental vari- ables via univariate spline transformations, Computational Statistics & Data Analysis, 16, 423–440.MathSciNetMATHCrossRefGoogle Scholar
  5. Durand, J. F. and Sabatier, R. (1994), Additive splines for PLS regression, Tech. Rept. 94–05,Unité de Biométrie, ENSAM-INRA-UM II, Montpellier, France. In press in Journal of the American Statistical Association.Google Scholar
  6. Escoufier, Y. (1987), Principal components analysis with respect to instrumental variables, European Courses in Advanced Statistics, University of Napoli, 285–299.Google Scholar
  7. Eubank, R. L. (1988), Spline smoothing and nonparametric regression, New York and Basel: Dekker. Frank, I. E., and Friedman, J. H. (1993), A statistical view of some Chemometrics regression tools (with discussion), Technometrics, 35, 109–148.Google Scholar
  8. Gifi, A. (1990), Nonlinear multivariate analysis, Chichester: Wiley.MATHGoogle Scholar
  9. IJastie, T. and Tibshirani, R. (1990), Generalized additive models. London: Chapman and Hall.Google Scholar
  10. Hastie, T. et al. (1994), Flexible discriminant analysis by optimal scoring, Journal of American Statistical Association, 89, 1255–1270.MathSciNetMATHCrossRefGoogle Scholar
  11. Ramsay, J. 0. (1988), Monotone regression splines in action (with discussion), Statistical Science, 3, 425–461.CrossRefGoogle Scholar
  12. Rao, C. R. (1964), The use and the interpretation of principal component analysis in applied research, Sankhya A, 26, 329–356.Google Scholar
  13. Wold, S. et al. (1983), The multivariate calibration problem in chemistry solved by the PLS method, Proc. Conf. Matrix Pencils. Ruhe, A. and Kagstrom, B. (Eds), Lecture notes in mathematics, Heidelberg: Springer Verlag, 286–293.Google Scholar

Copyright information

© Springer Japan 1998

Authors and Affiliations

  • Jean-François Durand
    • 1
    • 2
  1. 1.Probabilités et StatistiqueUniversité Montpellier IIMontpellierFrance
  2. 2.Unité de BiométrieENSAM-INRA-UM IIMontpellierFrance

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