论文标题
通过可调损失进行假设检验
On Hypothesis Testing via a Tunable Loss
论文作者
论文摘要
我们考虑了使用随机测试通过LIAO \ textit {et al}提出的可调损失函数的简单假设检验的问题。在此问题中，我们得出与Neyman-Pearson引理，Chernoff-Stein Lemma以及经典假设检验问题中的Chernoff信息相对应的结果。具体而言，我们证明了Neyman中问题的最佳错误指数 - 佩森的设置与经典结果一致。此外，我们提供了最佳贝叶斯误差指数的下限。
We consider a problem of simple hypothesis testing using a randomized test via a tunable loss function proposed by Liao \textit{et al}. In this problem, we derive results that correspond to the Neyman--Pearson lemma, the Chernoff--Stein lemma, and the Chernoff-information in the classical hypothesis testing problem. Specifically, we prove that the optimal error exponent of our problem in the Neyman--Pearson's setting is consistent with the classical result. Moreover, we provide lower bounds of the optimal Bayesian error exponent.
