Optimal generalized ridge estimator under the generalized cross-validation criterion in linear regression

In this short paper, we mainly aim to study the generalized ridge estimator in a linear regression model. Through matrix techniques including Hadamard product and derivative of a vector, the globally optimal generalized ridge estimator is derived under the generalized cross-validation criterion from the theoretical point of view. It will be seen that the notion of linearized ridge estimator plays an important role in the process. A numerical example is applied to illustrate the main results of the paper.