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We investigate the problem of distributed parameter estimation under the most stringent bandwidth constraint that each sensor quantizes its local observation into one bit of information. Conventional fixed quantization (FQ) approaches, which employ a fixed threshold for all sensors, incur an estimation error growing exponentially with the difference between the threshold and the unknown parameter to be estimated. To address this difficulty, we propose a distributed adaptive quantization (AQ) approach, where, with sensors sequentially broadcasting their quantized data, each sensor adaptively adjusts its quantization threshold using prior transmissions from other sensors. Specifically, three adaptive schemes are presented in this paper. The maximum likelihood (ML) estimators associated with these three AQ schemes are developed and their corresponding Cramer-Rao bounds (CRBs) are analyzed. The analysis shows that our proposed one-bit AQ approach can asymptotically attain an estimation variance as least as only pi/2 times that of the clairvoyant sample-mean estimator using unquantized observations. Numerical results are illustrated to show the effectiveness of the proposed approach and to corroborate our claim.