The advantages and limitations of coherent multiple-input multiple-output (MIMO) radar have been discussed widely. In practical systems, nonidealities often impose the dominant limitation to system performance. Consequently, successful high-performance systems typically employ adaptive techniques. Because of the higher potential performance of MIMO systems, they become even more sensitive to the system model if adaptivity is not employed. The quintessential example of the need for adaptivity is by ground-moving-target indictor (GMTI) radars, which employ space-time adaptive processing (STAP). As an initial step toward a more general study of test statistic robustness, we study an approximation to STAP, based on requiring test statistic invariance to clutter localization about an angle-Doppler operating point. We consider the effects of angle and velocity mismatch on clutter mitigation performance. Furthermore, we investigate the implications of MIMO waveform cross-antenna contamination by using invariance.