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Regression Splines for Multivariate Additive Modeling

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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.

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References

  • 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 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • Escoufier, Y. (1987), Principal components analysis with respect to instrumental variables, European Courses in Advanced Statistics, University of Napoli, 285–299.

    Google Scholar 

  • 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 

  • Gifi, A. (1990), Nonlinear multivariate analysis, Chichester: Wiley.

    MATH  Google Scholar 

  • IJastie, T. and Tibshirani, R. (1990), Generalized additive models. London: Chapman and Hall.

    Google Scholar 

  • Hastie, T. et al. (1994), Flexible discriminant analysis by optimal scoring, Journal of American Statistical Association, 89, 1255–1270.

    Article  MathSciNet  MATH  Google Scholar 

  • Ramsay, J. 0. (1988), Monotone regression splines in action (with discussion), Statistical Science, 3, 425–461.

    Article  Google Scholar 

  • Rao, C. R. (1964), The use and the interpretation of principal component analysis in applied research, Sankhya A, 26, 329–356.

    Google Scholar 

  • 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 

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© 1998 Springer Japan

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Durand, JF. (1998). Regression Splines for Multivariate Additive Modeling. In: Hayashi, C., Yajima, K., Bock, HH., Ohsumi, N., Tanaka, Y., Baba, Y. (eds) Data Science, Classification, and Related Methods. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65950-1_65

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  • DOI: https://doi.org/10.1007/978-4-431-65950-1_65

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-70208-5

  • Online ISBN: 978-4-431-65950-1

  • eBook Packages: Springer Book Archive

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