Continuity and Uniqueness of Regularized Output Least Squares Optimal Estimators

The continuity and uniqueness properties of optimal estimators with respect to data are considered for different regularizations. It is found that there is a weak stability for optimal estimators as set-valued mappings under a weak regularization. For stronger regularization results are obtained that give stability in stronger topologies and the finiteness of the set of optimal estimators. Finally, we give conditions that imply uniqueness of optimal estimators and Lipschitz continuity with respect to data.