We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from the distributions used in the likelihood ratio test, sequential probability ratio test, and Hoeffding's generalized likelihood ratio test in the composite setting. When the real distributions are within a small divergence ball of the test distributions, we find the deviation of the worst-case error exponent of each test with respect to the matched error exponent. In addition, we consider the case where an adversary tampers with the observation, again within a divergence ball of the observation type. We show that the tests are more sensitive to distribution mismatch than to adversarial observation tampering.
翻译:我们研究了 i. d. 分布 之间不匹配的二进位假设测试问题。 我们分析了当生成观测的实际分布不同于概率比测试、 顺序概率比测试以及 Hoffding 在复合环境下的通用概率比测试中使用的分布时, 对应差数的对比误差概率指数之间的权衡。 当实际分布在测试分布的微小差异球中时, 我们发现每次测试中最差的差数相对于匹配差数指数的偏差。 此外, 我们还考虑了对手篡改观察结果, 还是在观测类型差异球内的情况。 我们显示, 测试对分布不匹配比对对抗性观察的篡改更敏感 。