Second-Order Asymptotically Optimal Outlier Hypothesis Testing

We revisit the outlier hypothesis testing framework of Li et al. (TIT 2014) and derive fundamental limits for optimal test under generalized Neyman-Pearson criterion. In testing, one is given multiple observed sequences, where most sequences are generated i.i.d. from a nominal distribution. The task to discern set outlying that anomalous distributions. distributions xmlns:xlink="http://www.w3.org/1999/xlink">unknown . study tradeoff among probabilities misclassification error, false alarm reject tests satisfy weak conditions on rate decrease these error as function sequence length. Specifically, we propose threshold-based ensures exponential decay probabilities. two constraints probability, with constraint being it non-vanishing constant other has an rate. For both cases, characterize bounds threshold, each pair demonstrate optimality our first consider case at then generalize results number unknown can follow different