Some Algebraic Properties of Ridge Coefficients
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1980 · Volume 42 · Issue 1
DOI: 10.1111/j.2517-6161.1980.tb01097.x
Abstract
This note is concerned with one parameter ridge estimators in a multiple linear regression context as described by Hoerl and Kennard (Technometrics,12(1970), pp. 55-68). These estimators are rational functions of the ridge parameter, and some properties concerning sign changes and asymptotic behaviour are noted. Further properties of these estimators are derived assuming that thex'xmatrix possesses intraclass (or uniform) correlation structure. Some of these characteristics, e.g. the order of the ridge coefficients and their rates-of-change, are unrelated to the degree of multicollinearity; while others, e.g. existence and location of sign changes, are explicitly related to multicollinearity.
Keywords
ridge estimator, ridge trace, rational function, intraclass correlation, multicollinearity
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