  In this paper, we consider distributed maximum likelihood estimation (MLE)
with dependent quantized data under the assumption that the structure of the
joint probability density function (pdf) is known, but it contains unknown
deterministic parameters. The parameters may include different vector
parameters corresponding to marginal pdfs and parameters that describe
dependence of observations across sensors. Since MLE with a single quantizer is
sensitive to the choice of thresholds due to the uncertainty of pdf, we
concentrate on MLE with multiple groups of quantizers (which can be determined
by the use of prior information or some heuristic approaches) to fend off
against the risk of a poor/outlier quantizer. The asymptotic efficiency of the
MLE scheme with multiple quantizers is proved under some regularity conditions
and the asymptotic variance is derived to be the inverse of a weighted linear
combination of Fisher information matrices based on multiple different
quantizers which can be used to show the robustness of our approach. As an
illustrative example, we consider an estimation problem with a bivariate
non-Gaussian pdf that has applications in distributed constant false alarm rate
(CFAR) detection systems. Simulations show the robustness of the proposed MLE
scheme especially when the number of quantized measurements is small.
