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We study robust transceiver optimization in a downlink, multiuser, wireless system, where the transmitter and the receivers are equipped with antenna arrays. The robustness is defined with respect to imperfect knowledge of the channel at the transmitter. The errors in the channel state information are assumed to be bounded, and certain quality-of-service targets in terms of mean-square errors (MSEs) are guaranteed for all channels from the uncertainty regions. Iterative algorithms are proposed for the transceiver design. The iterations perform alternating optimization of the transmitter and the receivers and have equivalent semidefinite programming representations with efficient numerical solutions. The framework supports robust counterparts of several MSE-optimization problems, including transmit power minimization with per-user or per-stream MSE constraints, sum MSE minimization, min-max fairness, etc. Although the convergence to the global optimum cannot be claimed due to the intricacy of the problems, numerical examples show good practical performance of the presented methods. We also provide various possibilities for extensions in order to accommodate a broader set of scenarios regarding the precoder structure, the uncertainty modeling, and a multicellular setup.