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Continuum Regression: Cross-Validated Sequentially Constructed Prediction Embracing Ordinary Least Squares, Partial Least Squares and Principal Components Regression

M. Stone and R. J. Brooks
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 52, No. 2 (1990), pp. 237-269
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345437
Page Count: 33
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Continuum Regression: Cross-Validated Sequentially Constructed Prediction Embracing Ordinary Least Squares, Partial Least Squares and Principal Components Regression
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Abstract

The paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression. In the context of a general sequential procedure for doing this, it is shown that, with a particular objective criterion for the construction, the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum, with partial least squares lying in between. There are two adjustable `parameters' controlling the procedure: `alpha', in the continuum [ 0, 1], and `omega', the number of regressors finally accepted. These control parameters are chosen by cross-validation. The method is illustrated by a range of examples of its application.

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