Improvement of the mixed Liu estimator applying Jackknife method in linear regression models

In the presence of multicollinearity in the regression models, the ordinary least squares estimator loses its performance. Some solutions to reduce the effects of multicollinearity have been proposed, including the application of biased estimators such as Liu estimate and estimation under linear restrictions. But due to the Liu estimator being biased, the Jackknife method has been introduced to reduce the bias. In this paper, we will examine the Jackknifed Liu estimator and propose a new estimator under stochastic linear restrictions namely stochastic restricted Jackknifed Liu estimator. A simulation study is conducted to investigate the performance of this new estimator using two measures namely mean squared errors and absolute bias. From simulation study results, we find that the new estimator outperforms the OLS and Liu estimators, and it is superior to both OLS and Liu estimators, using the mean squared errors and absolute bias criteria.