Analysing of some biased estimators in linear regression and comparisons of the residuals of these estimators

In many applications in statistics, econometrics and finance, the analysts are usually uncertain about the validity of the prior information, so the common procedure is to (pre-) test Ho prior to estimating the parameters of the model. The sampling properties of these estimators of the parameters in a linear regression model, after a pre-test for linear restrictions on the coefficient vector, have been widely examined in the literature. In this thesis; a new biased estimator is proposed by combining the idea of preliminary test and characteristics of Liu estimator introduced by Liu(1993). In regression analysis, researchers often encounter the problem of multicollinearity. One of the solutions to this problem is to use the non-operational almost unbiased ridge regression estimator. In this thesis; general expressions are derived for the moments of the Lawless and Wang's operational almost unbiased ridge regression estimator. The residuals carry important information concerning the appropriateness of assumptions of the model and also play an important role in regression diagnostics. Therefore the residuals of some biased estimators are analyzed and compared with O.L.S. residuals in terms of mean-square error. Key Words: Preliminary test (pre-test) estimator, Liu estimator, residual, multicollinearity, biased estimation.