Nonparametric One-Bit Quantizers for Distributed Estimation

In this paper, we consider the nonparametric distributed parameter estimation problem using one-bit quantized data from peripheral sensors. Assuming that the sensor observations are bounded, nonparametric distributed estimators are proposed based on the knowledge of the first N moments of sensor noises. These estimators are shown to be either unbiased or asymptotically unbiased with bounded and known estimation variance. Further, the uniformly optimal quantizer based only on the first moment information and the optimal minimax quantizer with the knowledge of the first two moments are determined. The proposed estimators are shown to be consistent even when local sensor noises are not independent but m-dependent. The relationship between the proposed approaches and dithering in quantization is also investigated. The superiority of the proposed quantization/estimation schemes is illustrated via illustrative examples.