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Partial Least Squares Regression on Smooth Factors
Constantinos Goutis and Tom Fearn
Journal of the American Statistical Association
Vol. 91, No. 434 (Jun., 1996), pp. 627-632
Stable URL: http://www.jstor.org/stable/2291658
Page Count: 6
You can always find the topics here!Topics: Least squares, Matrices, Eigenvectors, Mathematical vectors, Calibration, Eigenvalues, Contour lines, Data smoothing, Error rates, Orthogonality
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In this article we present a modification of partial least squares regression to account for inherent nonexchangeabilities of the columns of the design matrix. In chemometrics applications it is common to write the matrix as a bilinear form of latent variables and loadings. These loadings are often interpreted as sampled values of functions; hence they should exhibit a degree of smoothness. Our method forces the partial least squares factors to be smooth, by using a roughness penalty motivated by nonparametric regression. We present a computational method to determine the loadings that guarantees a desired orthogonality at successive steps. We propose a cross-validatory choice of the smoothing parameter and the number of loadings. We illustrate the algorithm by an example and describe our experience with real data.
Journal of the American Statistical Association © 1996 American Statistical Association