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We consider the robust precoder design for multiuser multiple-input single-output (MU-MISO) systems where the channel state information (CSI) is fed back from the single antenna receivers to the centralized transmitter equipped with multiple antennas. We propose to compress the feedback data by projecting the channel estimates onto a vector basis, known at the receivers and the transmitter, and quantizing the resulting coefficients. The channel estimator and the basis for the rank reduction are jointly optimized by minimizing the mean-square error (MSE) between the true and the rank-reduced CSI. Expressions for the conditional mean and the conditional covariance of the channel are derived which are necessary for the robust precoder design. These expressions take into account the following sources of error: channel estimation, truncation for rank reduction, quantization, and feedback channel delay. As an example for the robust problem formulation, vector precoding (VP) is designed based on the expectation of the MSE conditioned on the fed-back CSI. Our results show that robust precoding based on fed-back CSI clearly outperforms conventional precoding designs which do not take into account the errors in the CSI.