Performance limits of hypothesis testing from vector-quantized data

We derive asymptotically tight bounds on the probabilities of type I and II errors of likelihood ratio tests with vector-quantized observations using large deviations error exponents. These bounds rely on losses in Kullback-Leibler distance between certain sources due to quantization. Asymptotic expressions for these losses are determined for a many-point quantizer. The quantizer that optimizes the receiver operating characteristic (ROC) curve is then derived under a tesselating cell assumption