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We consider distributed parameter estimation using quantized observations in wireless sensor networks (WSNs) where, due to bandwidth constraint, each sensor quantizes its local observation into one bit of information. A conventional fixed quantization (FQ) approach, which employs a fixed threshold for all sensors, incurs 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, which, with sensors sequentially broadcasting their quantized data, allows each sensor to adaptively adjust its quantization threshold. Three AQ schemes are presented: (1) AQ-FS that involves distributed delta modulation (DM) with a fixed stepsize, (2) AQ-VS that employs DM with a variable stepsize, and (3) AQ-ML that adjusts the threshold through a maximum likelihood (ML) estimation process. The ML estimators associated with the three AQ schemes are developed and their corresponding Cramer-Rao bounds (CRBs) are analyzed. We show that our 1-bit AQ approach is asymptotically optimum, yielding an asymptotic CRB that is only pi/2 times that of the clairvoyant sample-mean estimator using unquantized observations.