Regression Splines for Multivariate Additive Modeling
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.
KeywordsLinear Discriminant Analysis Discriminant Variable Spline Coefficient Common Principal Component Generalize Principal Component Analysis
Unable to display preview. Download preview PDF.
- 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
- 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. 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
- IJastie, T. and Tibshirani, R. (1990), Generalized additive models. London: Chapman and Hall.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