AN INVESTIGATION INTO PROPERTIES OF JACKKNIFED AND BOOTSTRAPPED LIU-TYPE ESTIMATOR

In 2003, Liu proposed a new estimator dealing with the problem of multicollinearity in linear regression model pointing out a drawback of ridge estimator used in this context. This new estimator, called Liu-type estimator was demonstrated to have lesser mean squared error than ridge estimator and ordinary least squares estimator, however, it may carry a large amount of bias. In the present paper, we propose different estimators in order to reduce the bias of Liu-type estimator, one using the Jackknife technique and other using the technique proposed in Kadiyala \cite{kad1984}. We also investigate the Bootstrap method of bias correction on the Liu-type estimator as well. The bias and mean squared error of these estimators have been compared using a simulation study as well as a numerical example. LSTA-2016-0059