Moment Estimation and Dithered Quantization

This letter examines the influence of low-bit quantization on moment estimators with special emphasis on the 1-bit case. Moment estimators are especially useful if no prior knowledge on the distribution of the observations is available or if an ML approach is analytically intractable or computationally infeasible. In order to arrive at analytical results for this very general case, we focus on a dithered quantization scheme that allows us to specify and analyze its asymptotic behavior. We show that consistency can be retained under mild conditions, and furthermore, we quantify the asymptotic variance. Additionally, we illustrate how to find an estimator that achieves the best performance possible in this scenario. Finally, we bolster our analytical results with simulations for the illustrative case of an AR(1) process and provide a comparison with undithered schemes. A conclusion summarizes this letter´s contribution and explores possible areas of application