  Estimation of a location parameter based on noisy and binary quantized
measurements is considered in this letter. We study the behavior of the
Cramer-Rao bound as a function of the quantizer threshold for different
symmetric unimodal noise distributions. We show that, in some cases, the
intuitive choice of threshold position given by the symmetry of the problem,
placing the threshold on the true parameter value, can lead to locally worst
estimation performance.
