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Yang and Huang have introduced a generalized Mahalanobis loss function which can be applied to the estimator for regression coefficients whether its covariance matrix is singular or non singular. In this paper, we give the detailed comparisons among those estimators that can be derived from the modified ridge principal component estimator under the generalized Mahalanobis loss function by the average loss criterion. Also, we obtain conditions for the superiority of one estimator over the others. Furthermore, two numerical examples are given to illustrate the theoretical results.

Further research on the modified ridge principal component estimator in linear model