Superiority of the Liu estimator over some estimators based on the likelihood loss function in linear regression model

This paper is concerned with the superiority of the Liu estimator under the Pitman's closeness criterion and the average loss criterion based on the likelihood loss function in linear regression model. The likelihood loss function is derived from the point of view of classification of two normal populations and can be considered as a combination of the generalized variance and the Mahalanobis loss function. The conditions for the superiority of the Liu estimator over the ordinary least squares estimator and the ridge estimator by the above two criteria based on the likelihood loss function are derived. Also, the conditions for the superiority of the ridge estimator over the ordinary least squares estimator under the above two criteria are given. Finally, a Monte Carlo simulation study is conducted to illustrate some of the theoretical results.