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The speech distortion weighted multichannel Wiener filter (SDW-MWF) is a promising multi-microphone noise reduction technique, in particular for hearing aid applications. Its benefit over other single- and multi-microphone techniques has been shown in several previous contributions, theoretically as well as experimentally. In theoretical studies, it is usually assumed that there is a single target speech source. The filter can then be decomposed into a conceptually interesting structure, i.e., into a spatial filter (related to other known techniques) and a single-channel postfilter, which then also allows for a performance analysis. Unfortunately, it is not straightforward to make a robust practical implementation based on this decomposition. Instead, a general SDW-MWF implementation, which only requires a (relatively easy) estimation of speech and noise correlation matrices, is mostly used in practice. This paper features a theoretical study and experimental validation on a binaural hearing aid setup of this standard SDW-MWF implementation, where the effect of estimation errors in the second-order statistics is analyzed. In this case, and for a single target speech source, the standard SDW-MWF implementation is found not to behave as predicted theoretically. Second, two recently introduced alternative filters, namely the rank-one SDW-MWF and the spatial prediction SDW-MWF, are also studied in the presence of estimation errors in the second-order statistics. These filters implicitly assume a single target speech source, but still only rely on the speech and noise correlation matrices. It is proven theoretically and illustrated through experiments that these alternative SDW-MWF implementations behave close to the theoretical optimum, and hence outperform the standard SDW-MWF implementation.