In multi-user multiple-input single-output orthogonal frequency-division multiplexing(MISO-OFDM) downlinks with limited feedback,both linear precoders(LP) and Tomlinson-Harashima precoders(THP) experience performance degradation due to inaccurate channel state information at the transmitter(CSIT).This analysis treats the downlink channels as random quantities and exploits their second order statistics in robust precoding schemes to correct the errors introduced in the feedback procedure.The time-domain channel vectors are found to reduce the feedback overhead more than the frequency-domain vectors.A compression and restoration method and a codebook design are also given to obtain compact feedback quantities.Simulations show that the robust LP and THP are superior to the previous methods with tradeoffs possible between performance and feedback overhead. In multi-user multiple-input single-output orthogonal frequency-division multiplexing (MISO-OFDM) downlinks with limited feedback, both linear precoders (LP) and Tomlinson-Harashima precoders (THP) experience performance degradation due to inaccurate channel state information at the transmitter (CSIT) .This analysis treats the downlink channels as random quantities and exploits their second order statistics in robust precoding schemes to correct the errors introduced in the feedback procedure. time-domain channel vectors are found to reduce the feedback overhead more than the frequency-domain vectors. A compression and restoration method and a codebook design are also given to obtain compact feedback quantities. Simulations show that the robust LP and THP are superior to the previous methods with tradeoffs possible between performance and feedback overhead.