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We consider distributed parameter estimation in a wireless sensor network, where due to bandwidth constraint, all sensor nodes have to quantize their observations and send quantized data to a fusion center. We consider the case where each sensor can send only one bit of information. In such a case, the achievable estimation performance is critically dependent on the choice of the one-bit quantizer used at the sensor nodes to perform quantization; it is also known that a fixed quantizer does not perform well, in particular when the quantization threshold is away from the unknown parameter to be estimated. In this paper, we propose a new distributed adaptive quantization scheme by which each individual sensor node dynamically adjusts the threshold of its quantizer based on earlier transmissions from other sensor nodes. We develop the maximum likelihood estimator (MLE) and derive the Cramer-Rao bound (CRB) associated with our distributed adaptive quantization scheme. Numerical results show that our approach does not suffer from the drawback of the fixed quantization approach and outperforms the latter.