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.

中文翻译：

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不匹配二元假设检验：误差指数敏感性

我们研究了 iid 分布之间不匹配的二元假设检验问题。当生成观察的实际分布与复合设置中的似然比检验、序列概率比检验和 Hoeffding 的广义似然比检验中使用的分布不同时，我们分析了成对误差概率指数之间的权衡。当真实分布在测试分布的一个小散度球内时，我们发现每个测试的最坏情况误差指数相对于匹配误差指数的偏差。此外，我们考虑了对手篡改观察的情况，同样在观察类型的发散球内。我们表明，与对抗性观察篡改相比，测试对分布不匹配更敏感。