Consistency of weighted least-square estimators for parameter estimation problems based on binary measurements

In this paper, we present a new weighted least-squares (WLS) approach for parameter estimation based on binary data. Two WLS criteria are studied. We show that these two criteria do not have the same asymptotical behavior although they are closely related. Particularly, in the presence of noise, one of the criteria used for determining the system parameters provides an appropriate estimation, whereas the other one leads to an underestimation of the system parameters. These asymptotical results are illustrated by simulations in Gaussian and non-Gaussian contexts.