The Effect of Uniform Quantization on Parameter Estimation of Compound Distributions

This letter considers the problem of how uniform quantization affects the maximum likelihood estimation of the parameters of a probability density function representing a compound distribution. As a measure of the information loss due to quantization, the loss of Fisher information is used. The main contribution of this letter is the approximation which characterizes the asymptotic behavior of the loss allowing a significant reduction of the computational complexity. We further investigate how to choose the quantization interval to guarantee a predefined loss of Fisher information. An extensive numerical simulation demonstrates the efficiency of the approximation.