Anomalies persist in the foundations of ridge regression as set forth in Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and their properties do not follow on constraining lengths of solution vectors using LaGrange’s method, as claimed. Estimators so constrained have singular distributions; the proposed solutions are not necessarily minimizing; and heretofore undiscover...

The main thrust of this paper is to investigate the ridge regression problem in multicollinear data. The properties of ridge estimator are discussed. Variance inflation factors, eigen values and standardization problem are studied through an empirical comparison between OLS and ridge regression method by regressing number of persons employed on five variables. Methods to choose biasing paramete...

Ridge regression is often the method of choice in ill–conditioned systems. A canonical form identifies regions in the parameter space where Ordinary Least Squares (OLS) is problematic. A curious but unrecognized property of ridge solutions emerges: Under spherical errors with or without moments, the relative concentrations of the canonical estimators reverse as the ridge scalar evolves, the est...

Anomalies persist in the foundations of ridge regression as set forth in Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and their properties do not follow on constraining lengths of solution vectors using LaGrange’s method, as claimed. Estimators so constrained have singular distributions; the proposed solutions are not necessarily minimizing; and heretofore undiscover...

We consider the application of a popular penalised regression method, Ridge Regression, to data with very high dimensions and many more covariates than observations. Our motivation is the problem of out-of-sample prediction and the setting is high-density genotype data from a genome-wide association or resequencing study. Ridge regression has previously been shown to offer improved performance ...