Abstarct: In this thesis, the uncertain prior (non-sample) information has been used in penalized linear (ridge and LASSO) and robust penalized linear (M ridge) models, which are resulted in preliminary test, shrinkage Stein-type and its positive rule estimators. The characteristics of these estimators have been derived by considering some linear restrictions on the parameter space. Also, the available auxiliary information has helped the estimation procedure to obtain shrinkage estimators, when outliers and leverage points in dataset are present. In all above models, the achieved results are validated by some simulation studies and real data analyses. The results confirm the introduced shrinkage estimators outperform the natural estimators in the aforementioned specific models.