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In this paper, the problem of distributed parameter estimation in a wireless sensor network is considered, where due to bandwidth constraint, each sensor node sends only one bit of information per sample to a fusion center. 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. The maximum likelihood estimator (MLE) and the Cramer-Rao bound (CRB) associated with our distributed adaptive quantization scheme are derived. Numerical results depicting the performance and advantages of our approach over a fixed quantization scheme are presented.