Superiority of the MCRR Estimator Over Some Estimators In A Linear Model

Modied (r, k) class ridge regression (MCRR) which includes unbiased ridge regression (URR), (r, k) class, principal components regression (PCR) and the ordinary least squares (OLS) estimators is proposed in regression analysis, to overcome the problem of multicollinearity. In this paper, we derive the necessary and sucient conditions for the superiority of the MCRR estimator over each of these estimators under the Mahalanobis loss function by the average loss criterion. Then, we compare these estimators with each other using the same criterion. Finally, a numerical example is done to illustrate the theoretical results.Key Words: Multicollinearity; Ordinary Ridge Regression Estimator; (r, k) Class Estimator; MCRR estimator; Mahalanobis loss function.