We analyze the asymptotic performance of rate adaptation for Transmit Antenna Selection (TAS) and Maximum Eigenmode Beamforming (MEB) schemes in Multiple-Input Multiple-Output (MIMO) systems under imperfect channel state information (CSI) and feedback delay. The rate is adapted according to a target outage probability. We derive lower and upper bounds to this rate. We also asymptotically characterize the multi-step prediction error when MMSE prediction is used to combat feedback delay. Using the bounds and the prediction error asymptotics, we show that the rate gap from the ideal CSI scenario asymptotically grows logarithmically with SNR. The slope is at most the target outage probability. We find that when the target outage probability is decreased faster than an identified growth rate and prediction error goes to zero, then the rate gap remains bounded. ©2010 IEEE.