In practical systems, the design of linear MIMO transceivers should be robust to partial or imperfect channel state information (CSI). This paper considers the case in which only the second-order statistics of the channel is known at the transmitter while the receiver has a perfect CSI. In such a case, it is possible to optimally design robust MIMO transceivers 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 regime to obtain simple optimization problems that can be readily solved. Numerical examples show substantial gains compared to other methods.