The role of MVU estimator and CRB in binary composite hypothesis test

This work presents a new perspective to the relationship between the composite binary hypothesis test and the estimation of its unknown parameters, i.e. the Uniformly Most Powerful (UMP) test and the Minimum Variance and Unbiased Estimator(MVUE). We show that for the one-sided binary composite hypothesis test, if the UMP test exists, it is nothing but comparing the MVUE for the unknown parameter with a threshold. The paper tries to make a link between the Cramer Rao Bound (CRB) in estimation theory and the UMP performance bound in detection theory. In addition to the intrinsic theoretical interest of such relationship discussed in the paper, it leads us to proposing a novel detection method. For such problems in which the UMP test does not exist, we suggest using a good estimator of the unknown parameter as the decision statistic. The simulation results confirm the idea that the closer we get to the CRB in estimating the unknown parameter, the more we get near to the UMP performance bound in detection.