Marginal maximum likelihood estimation methods for the tuning parameters of ridge, power ridge, and generalized ridge regression

Abstract

This study introduces fast marginal maximum likelihood (MML) algorithms for estimating the tuning (shrinkage) parameter(s) of the ridge and power ridge regression models, and an automatic plug-in MML estimator for the generalized ridge regression model, in a Bayesian framework. These methods are applicable to multicollinear or singular covariate design matrices, including matrices where the number of covariates exceeds the sample size. According to analyses of many real and simulated datasets, these MML-based ridge methods tend to compare favorably to other tuning parameter selection methods, in terms of computation speed, prediction accuracy, and ability to detect relevant covariates.