Computational Method for Jackknifed Generalized Ridge Tuning Parameter based on Generalized Maximum Entropy

Abstract

In this article, a new method to estimate the Jackknifed generalized ridge tuning parameter, based on the Jackknifed Ridge-trace and an analytical method borrowed from generalized maximum entropy, is presented. The ideas in the article are illustrated and evaluated using to the well-known Portland cement data set and simulations.

Ridge Regression and Generalized Maximum Entropy: An improved version of the Ridge–GME parameter estimator

“…The improvement accomplished in this paper overcomes this weakness of the original Ridge-GME parameter estimator. The simulation study and the empirical applications discussed in this paper, as well as the results obtained by Macedo et al (2010) and Erdugan and Akdeniz (2012), reveal a good performance of this Ridge Regression procedure in the case of regression models with small samples sizes affected by collinearity.…”

“…The Ridge-GME parameter estimator was introduced by Macedo et al (2010) and was adapted for a jackknife procedure by Erdugan and Akdeniz (2012). The basic idea underlying the Ridge-GME parameter estimator is to combine the ridge trace and the GME estimator.…”

“…In answering to these questions, Macedo et al (2010) illustrate how the Ridge-GME parameter estimator can be implemented. Moreover, based on the results from the simulation studies conducted by Macedo et al (2010) and Erdugan and Akdeniz (2012), it seems reasonable to state that, in the case of regression models with small samples sizes affected by collinearity, the Ridge-GME parameter estimator has a good performance and it may be recommended to practitioners.…”

“…In this case, the ridGME code (the MATLAB code provided as supplementary material) presents the ridge trace to help the user in the selection of the ridge interval.6 For example, based on the same ridge trace for the Portland cement model, different supports for the parameters are considered byMacedo et al (2010) andErdugan and Akdeniz (2012).…”