Construction Concepts for Continuum Regression

Approaches for meaningful regressor construction in the linear prediction problem are investigated in a framework similar to partial least squares and continuum regression, but weighted to allow for intelligent specification of an evaluative scheme. A cross-validatory continuum regression procedure is proposed, and shown to compare well with ordinary continuum regression in empirical demonstrations. Similar procedures are formulated from model-based constructive criteria, but are shown to be severely limited in their potential to enhance predictive performance. By paying careful attention to the interpretability of the proposed methods, the paper addresses a long-standing criticism that the current methodology relies on arbitrary mechanisms.