Admissibility of the linear estimators

The least squares estimator to be a poor estimator when the presence of multicollinearity in the multiple linear regression model. To overcome the problem of multicollinearity, new biased estimators have been proposed alternatively to the ordinary least squares estimator. Since there are many biased estimator, the admissibility of these estimators is examined.In this study, the r-k class, the ridge regression, the principal components and the ordinary least squares estimators are compared with each other under the Mahalanobis loss function. Then the generalized Liu and the Liu estimators compared to the ordinary least squares estimator under the Mahalanobis loss and Fisherian loss functions.