Some issues of shrinkage estimators in regression model in existence of multicollinearity

In this thesis, a new biased estimator is proposed to reduce the effect of high variance of the estimators as well as to over come the multicollineatry problem called modified unbiased ridge regression estimator. This thesis studies on the biased estimations which can help to reduce the effect of high variance of the estimators as well as to overcome the multicollinearity problem by conducting a comprehensive review of the biased estimators present in previous literature. Furthermore, new biased estimators are proposed in linear regression model called "modified unbiased ridge regression estimator" (MURRE) and "modified ridge two parameters estimator" (MRTP) based on "modified unbiased ridge regression" (MUR) was proposed in the study of Batah and Gore (2009). The performance of MURRE and MRTP are compared to some biased estimators theoretically based on the mean squares error (MSE) as a measure for goodness of fit. By simulation study and some theorems, here, the MURRE and MRTP estimators have good properties compared with some other biased estimators based on a simulation study. A numerical example has been considered to illustrate the performance of the estimators.