A Critique of Some Ridge Regression Methods

Abstract

Ridge estimates seem motivated by a belief that least squares estimates tend to be too large, particularly when there is multicollinearity. The ridge solution is to supplement the data by stochastically shrinking the estimates toward zero. Although flexibility is provided by the abstention from exact exclusion restrictions, ridge regression retains many weaknesses of similarly motivated procedures : a neglect of the basic fact that linear transformations should not change the implicit estimates of a model's coefficients, an incorrect labeling of nonorthogonal data as weak, and a loose representation of a priori beliefs and reliance at times on ad hoc pseudoinformation.

Key Words:

• Ridge regression
• Multicollinearity
• Principal components