On the limitations of Barankin type bounds for MLE threshold prediction

Various approximations of the Barankin bound (BB), called Barankin type bounds (BTBs), are usually used to predict the threshold region of the maximum likelihood estimator (MLE). In this paper, we show that BTBs are not always appropriate for predicting this threshold region. We prove that in some common estimation problems the BB is infinite, and thus, its approximations cannot reliably predict the MLE threshold region. This result is illustrated for two general signal processing models, in which BTBs can become arbitrarily large, and consequently, cannot reliably predict the MLE threshold region.