Redundant multirate filter bank transceivers have been proposed for block-based transmission over channels whose characteristics are known at both the receiver and the transmitter. We propose a criterion for the design of such transceivers for applications in which the channel is not known at the transmitter. The design objective is the minimization of the average mean square error of the data estimates produced by a zero-forcing equalizer over a statistically modelled class of channels. Two solution methods are proposed, one of which appears to be amenable to modification for the solution of certain other robust performance problems. It is shown that the optimal transmitter provides substantially improved performance over a scheme based on multicarrier modulation.