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For small-sized arrays such as hearing aids, noise reduction is obtained at the expense of an increased sensitivity to errors in the assumed signal model, i.e., microphone mismatch, variations in speaker and microphone positions, reverberation. However, the noise reduction algorithm should still be robust, i.e., insensitive to small signal model errors. In this paper, we evaluate the robustness of the Generalized Sidelobe Canceller (GSC) and a recently developed Multichannel Wiener Filtering (MWF) technique for hearing aid applications both analytically and experimentally. The analysis reveals that robustness of the GSC is especially crucial in complicated noise scenarios and that microphone mismatch is particularly harmful to the GSC, even when the adaptive noise canceller is adapted during noise only. Hence, a constraint on the noise sensitivity of the GSC is essential, at the expense of less noise reduction. The MWF on the other hand, is not affected by microphone mismatch and has a potential benefit over the robust GSC with noise sensitivity constraint. However, the MWF is sensitive to the estimation accuracy of the second order statistics of speech and noise so that its benefit may be lost in nonstationary noise scenarios.