The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose moments are centered around the empirical moments obtained from training samples. The goal is to design a test that performs well under all distributions in the uncertainty sets, i.e., minimize the worst-case error probability over the uncertainty sets. In the finite-alphabet case, the optimal test is obtained. In the infinite-alphabet case, a tractable approximation to the worst-case error is derived that converges to the optimal value using finite samples from the alphabet. A test is further constructed to generalize to the entire alphabet. An exponentially consistent test for testing batch samples is also proposed. Numerical results are provided to demonstrate the performance of the proposed robust tests.

翻译：本文研究鲁棒二元假设检验问题。在两种假设下，假设数据生成分布属于通过矩构造的不确定性集；特别地，这些集合包含矩中心位于训练样本经验矩附近的分布。目标是设计一种能在不确定性集中所有分布下表现良好的检验方法，即最小化不确定性集上的最坏情况误差概率。对于有限字母表情形，获得了最优检验。对于无限字母表情形，推导了最坏情况误差的可处理近似值，该近似值利用有限字母表样本收敛到最优值，并进一步构造了能推广到整个字母表的检验方法。此外，还提出了用于检验批次样本的指数一致性检验方法。数值结果验证了所提鲁棒检验方法的性能。