Further results on tradeoffs between detection and estimation

For a general discrete parameter signal model and a false alarm constraint, the authors give a general theorem which specifies lower bounds on worst-case probability of miss, worst-case probability of incorrectly specifying the number of parameters (order selection), and worst-case probability of parameter estimation error. These bounds are achievable by constrained min-max decision rules: the constrained min-max detector, the constrained min-max order selector, and the constrained min-max parameter estimator, respectively. As in previous work, the authors use the theory to study fundamental tradeoffs between achievable estimation, order selection, and detection performance for a multiple component signal model. Numerical results indicate that for the example studied, parameter estimation optimality entails very little loss in detection performance, while detection optimality severely sacrifices parameter estimation performance