This paper considers the robust design of a linear transceiver with imperfect channel state information (CSI) at the transmitter of a MIMO link. The framework embraces the design problem when CSI at the transmitter consists of the channel mean and covariance matrix or, equivalently, the channel estimate and the estimation error covariance matrix. The design of the linear MIMO transceiver is based on a general cost function covering several well known performance criteria. In particular, two families are considered in detail: Schur-convex and Schur-concave functions. Approximations are used in the low SNR and high SNR regimes separately to obtain simple optimization problems that can be readily solved. Numerical examples show gains compared to other suboptimal methods.