  This paper considers estimation of a quantized constant in noise when using
uniform and nonuniform quantizers. Estimators based on simple arithmetic
averages, on sample statistical moments and on the maximum-likelihood procedure
are considered. It provides expressions for the statistical efficiency of the
arithmetic mean by comparing its variance to the proper Cram\'er-Rao lower
bound. It is conjectured that the arithmetic mean is optimal among all
estimators with an exactly known bias. Conditions under which its statistical
performance are improved by the other estimation procedures when the exact bias
is not known are found and analyzed. Using simulations and analysis of
experimental data, it is shown that both moment-based and
maximum-likelihood-based estimators provide better results, when the noise
standard deviation is comparable with the quantization step and the noise model
of quantization can not be applied.
