Continuum Regression: Cross-Validated Sequentially Constructed Prediction Embracing Ordinary Least Squares, Partial Least Squares and Principal Components Regression
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1990 · Volume 52 · Issue 2
DOI: 10.1111/j.2517-6161.1990.tb01786.x
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.
Keywords
cross-validation, least squares prediction, partial least squares, principal components regression, sequential
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