Pace Regression

Abstract

This paper articulates a new method of linear regression, “pace regression”, that addresses many drawbacks of standard regression reported in the literature-particularly the subset selection problem. Pace regression improves on classical ordinary least squares (OLS) regression by evaluating the effect of each variable and using a clustering analysis to improve the statistical basis for estimating their contribution to the overall regression. As well as outperforming OLS, it also outperforms-in a remarkably general sense-other linear modeling techniques in the literature, including subset selection procedures, which seek a reduction in dimensionality that falls out as a natural byproduct of pace regression. The paper defines six procedures that share the fundamental idea of pace regression, all of which are theoretically justified in terms of asymptotic performance. Experiments confirm the performance improvement over other techniques.