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Continuum regression: Cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and principal components regression. (English) Zbl 0708.62054
Authors’ summary: The paper addresses the evergreen problem of construction of regressors for use in least squares muliple 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.
Reviewer: J.Lillestøl

MSC:
62J05 Linear regression; mixed models
62L12 Sequential estimation
62H25 Factor analysis and principal components; correspondence analysis
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