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This letter analyzes the performance of several typical one-bit universal distributed estimation schemes (DESs) in bandwidth-constrained sensor networks. We theoretically obtain the mean and mean-square error (MSE) of the DES based on binary form (BF) of the observation along with the MSE upper bound. It is proved that in some cases, the BF-based DES has larger MSE than the DES based on the complementary cumulative distribution function (CCDF) of the observation. Moreover, performance analysis is presented for the CCDF-based and BF-based DESs employing probabilistic quantization, respectively.