Generalized Cross-Validation for Simultaneous Optimization of Tuning Parameters in Ridge Regression

Abstract

When multicollinearity exists in the context of robust regression, ridge rank regression estimator can be used as an alternative to the rank estimator. Performance of the ridge rank regression estimator is highly dependent on the ridge parameter, here the tuning parameter. On the other hand, suppose we are provided with some non-sample uncertain prior information (UPI) about regression coefficients. Shrinkage estimation is a well-known strategy to improve estimation, under the UPI, where the amount of shrinkage is controlled by a tuning parameter. Hence, optimization of both tuning parameters can be a problem of interest. In this study, theoretical development of the generalized cross-validation (GCV) is considered and some numerical illustrations are given to validate the theoretical findings. Our results demonstrated that using the proposed GCV criterion, the shrinkage ridge rank regression estimator behaves well in the sense of minimum risk function.