Score-Function Quantization for Distributed Estimation

We study the problem of quantization for distributed parameter estimation. We propose the design of score-function quantizers to optimize different metrics of estimation performance. Score-function quantizers are a class of quantizers known to maximize the Fisher information for a fixed value of parameter thetas. We show that for distributions that satisfy a monotonicity property, the class of score-function quantizers can be made independent of parameter thetas. We then propose a generic algorithm to obtain the optimal Score-function quantizer that can be used to maximize three different metrics; minimum Fisher information, Bayesian Fisher information and minimum asymptotic relative efficiency. Through numerical examples, we illustrate that these algorithms converge to the optimal quantizers obtained through known algorithms for maximin ARE and Bayesian Fisher information.