The treatment of channel state information (CSI) is critical in the design of MIMO systems. Accurate CSI at the transmitter is often not possible or may require high feedback rates. Herein, we consider the robust design of linear MIMO transceivers with perfect CSI either at the transmitter or at both sides of the link. The framework considers the design problem where the imperfect CSI consists of the channel mean and covariance matrix or, equivalently, the channel estimate and the estimation error covariance matrix. The robust transceiver design is based on a general cost function of the average MSEs as well as a design with individual MSE based constraints. In particular, a lower bound of the average MSE matrix is explored for the design when only the CSI at the transmitter is imperfect. Under different CSI conditions, the proposed robust transceivers exhibit a similar structure to the transceiver designs for perfect CSI, but with a different equivalent channel and/or noise covariance matrix.