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：对稳健的二元假设测试问题进行了研究。在两种假设下,数据生成分布假定属于通过瞬间构造的不确定数据集;特别是,数据集包含分布,其时间围绕从培训样品中获得的经验时刻。目的是设计一个测试,在不确定数据集的所有分布下运行良好,即最大限度地减少不确定数据集的最大误差概率。在有限的阿尔法贝特案例中,最佳测试是获得的。在无限的阿尔法贝特案例中,得出最坏错误的可移植近似值,用字母表中的限定样品与最理想值相匹配。进一步构建一个测试,以概括整个字母。还提议对批量样本进行指数一致的测试。提供了数字结果,以显示拟议稳健测试的性能。