Publication: Second-order asymptotics of Hoeffding-like hypothesis tests
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2022-11-01
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IEEE
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Abstract
We consider a binary statistical hypothesis testing problem, where n independent and identically distributed random variables Z^n are either distributed according to the none 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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Proceedings of: 2022 IEEE Information Theory Workshop (ITW), 01-09 November 2022, Mumbai, India.
Keywords
Hoeffding test, Hypothesis testing, Information theory, Second-order asymptotics
Bibliographic citation
Harsha, K. V., Ravi, J. & Koch, T. (01-09 November 2022). Second-order asymptotics of Hoeffding-like hypothesis tests [proceedings]. 2022 IEEE Information Theory Workshop (ITW), Mumbai, India.