On Hypothesis Testing via a Tunable Loss
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We consider a problem of simple hypothesis testing using a randomized test via a tunable loss function proposed by Liao 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.
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