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The ridge regression approach can also be applied to deal with multicollinearity in the seemingly unrelated regression equations (SURE) models. However, to get the ridge-type estimators of the coefficients in a SURE model, choosing the ridge parameter has always been an important and challenging task. Herein, to cope with this issue, an optimal choice of the ridge parameter is proposed based on the generalized cross-validation (GCV) criterion. Moreover, some existing estimators of this parameter, in the context of the ordinary ridge regression models, are extended to be used in the SURE models. All these estimators, including the proposed and extended ones, and several state-of-the-art alternatives (altogether 36 different estimators) are compared with each other in terms of the GCV criterion. Lastly, an application of the methodology is given on chronic renal failure effect data.

A Monte Carlo study on the ridge parameter of the seemingly unrelated ridge regression models