Abstarct: In this thesis we consider the problem of estimating the p-dimensional location parameter in spherically symmetric models. The scale component is assumed to be known and unknown. Three restrictions are imposed on the vector parameter θ. First we asaume that all elements of θ are nonnegative, at the second hand it is assumed that only a subset of elements is nonnegative. Lastly, we deal with the situation where the parameter θ belongs to a cone C of R^p. We propose a class of shrinkage estimators wich dominates the natural estimator of θ under the quadratic and weighted quadratic loss functions.