Testing Against Independence and a R\'enyi Information Measure

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Publication date: 28 May 2018

Abstract: The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability distribution or an unknown product distribution. The empirical mutual information test, the Hoeffding test, and the generalized likelihood-ratio test are all shown to be asymptotically optimal. An expression based on a Renyi measure of dependence is shown to be the Fenchel biconjugate of the error-exponent function obtained by fixing one error exponent and optimizing the other. An example is provided where the error-exponent function is not convex and thus not equal to its Fenchel biconjugate.

Has companion code repository: https://github.com/pfistchr/arxiv-1805.11059

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