Optimum Quantization for Local Decision Based on Independent Samples

The problem of designing quantizers for use in decision-making systems is considered. Applying the theory of local tests, general criteria are derived for the optimal selection of quantizer parameters for the large-sample-size case. These criteria agree with previously established results based on optimization in terms of distance measures and are shown also to lead to that quantizer-decision system which is most efficient asymptotically. To illustrate the design procedure, several applications to signal detection are discussed.