Efficient estimates in regression models with highly correlated covariates

The specification of accurate ridge estimates in penalized regression models strongly depends on the appropriate choice of the tuning parameter which monitors the regularization process. In this work, we propose the selection of this parameter via the minimization of an extrapolation estimate of the generalized cross-validation function. The efficiency of the estimate is characterized by an appropriately defined index of proximity; in case that its value approaches one, the estimation becomes optimal. We consider regression models with highly correlated covariates and prove that the probability of the index of proximity being close to one is high. This result is confirmed through several simulation tests. (C) 2019 Elsevier B.V. All rights reserved.