A study on jackknifed estimators in regression model in presence of multicollinearity

Many researchers developed the biased estimation for reducing the impact of the multicollinearity problem in multiple linear regression but not using the Jackknife technique. The Jackknife biased estimation studied and over come the multicollinearity problem to determine the best estimator has good properties as well as to examined by conducting a comprehensive review of the Jackknife estimators present in previous literature. This thesis is based on applied Jackknife teachnique in biased estimator to reduce the baisedness as well as reduce the effect of high variance of these estimators in multiple linear model. Furthermore, a new estimator has been proposed in the multiple linear regression model called the "improved Jackknife Liu type estimator (IJLTE)" based on the Jackknife Liu type estimator (JLTE). The performance of IJLTE compared to some biased estimators theoretically is proofed based on the mean squares error (MSE) as a measure for goodness of fit. The IJLTE estimator has good characteristics compared with different biased estimators that have been proved when simulating some theorems. A simulation study as well as a numerical example between the Jackknifed biased estimators and the biased estimators has been done to determine the good estimator from these families based on mean sequare error criteria (MSE).