Shrinkage Difference-Based Liu Estimators In Semiparametric Linear Models

In this article, under a multicollinearity setting, we define difference-based Liu and non-Liu type shrinkage estimators along with their positive parts in the semiparametric linear model, when the errors are dependent and some nonstochastic linear restrictions are imposed. We derive the biases and exact risk expressions of these estimators and obtain the region of optimality of each estimator. Also, necessary and sufficient conditions, for the superiority of the difference-based Liu estimator over its counterpart, for choosing the Liu parameter d are established. Finally, we illustrate the performance of these estimators with a simulation study.