Abstarct: One of the important issues in theoretical statistics is the estimation and studying of their specifications on unknown parameters of the statistical models. About the estimation, estimators are compared together by different items like: bias, risk, efficiency and …; one of the items which is mostly ecognized by the investig to s, is the level of estim to s„s isk under specific loss function. In other words, the lower the risk the better the estimator would be. Using old known information in statistical models is usually considered as a term which at last results in restricted models. The estimator, created by restricted models is called restricted estimator (RE). In this thesis for the normal and multivariate normal models, the constrained Bayes estimator (CEB) and other types of estimators like: preliminary test estimator (PTE) and the constrained empirical Bayes estimator (CEBE) (in some parts) are considered and their risks are compared together.