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.