Second-Order Asymptotics of Hoeffding-Like Hypothesis Tests
2022 IEEE Information Theory Workshop (ITW)(2022)
摘要
We consider a binary statistical hypothesis testing problem, where n independent and identically distributed random variables Z
n
are either distributed according to the null hypothesis P or the alternate hypothesis Q, and only P is known. For this problem, a well-known test is the Hoeffding test, which accepts P if the Kullback-Leibler (KL) divergence between the empirical distribution of Z
n
and P is below some threshold. In this paper, we consider Hoeffding-like tests, where the KL divergence is replaced by other divergences, and characterize, for a large class of divergences, the first and second-order terms of the type-II error for a fixed type-I error. Since the considered class includes the KL divergence, we obtain the second-order term of the Hoeffding test as a special case.
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关键词
tests,second-order,hoeffding-like
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