On the performance of principal component Liu-type estimator under the mean square error criterion (Q1791355)

Summary: We [Research on the properties of parameter estimation in linear regression model. Chongqing, China: Chongqing University (PhD Thesis) (2013)] proposed an estimator, principal component Liu-type estimator, to overcome multicollinearity. This estimator is a general estimator which includes ordinary least squares estimator, principal component regression estimator, ridge estimator, Liu estimator, Liu-type estimator, \(r\)-\(k\) class estimator, and \(r\)-\(d\) class estimator. In this paper, firstly we use a new method to propose the principal component Liu-type estimator; then we study the superior of the new estimator by using the scalar mean squares error criterion. Finally, we give a numerical example to show the theoretical results.