Variations on Ridge Traces in Regression

Abstract

Ridge regression, perturbing the design moment matrix via a parameter k, persists in the study of ill-conditioned systems. Ridge traces, exhibiting solutions as functions of k, are intended to reflect stability as k evolves, in contrast to transient instabilities in ordinary least squares. This study examines derivative traces as analytic tools regarding stability, and develops rational representations for them. Two further gauges of stability are derivatives of variances of the ridge solutions, and the variances of the derivative traces. In contrast to ridge traces and their derivatives, neither of the latter depends on observed responses, and both support deterministic assessments.

Keywords:

• Derivative traces
• Deterministic traces
• Ill–conditioned models
• Ridge regression
• Stability of ridge traces

Mathematics Subject Classification:

• Primary: 62J07
• Secondary: 62J20

Acknowledgments

Research of the first author supported in part by the Department of Mathematics, University of Virginia.