First- and second-order hypothesis testing for mixed memoryless sources

Te Sun Han, Ryo Nomura*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The first- and second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under the constraint that the type I error probability is allowed asymptotically up to ε, is called the ε-optimum exponent. In this paper, we first give the second-order ε-optimum exponent in the case where the null hypothesis and alternative hypothesis are a mixed memoryless source and a stationary memoryless source, respectively. We next generalize this setting to the case where the alternative hypothesis is also a mixed memoryless source. Secondly, we address the first-order ε-optimum exponent in this setting. In addition, an extension of our results to the more general setting such as hypothesis testing with mixed general source and a relationship with the general compound hypothesis testing problem are also discussed.

Original languageEnglish
Article number174
Issue number3
Publication statusPublished - 2018 Mar 1
Externally publishedYes


  • General source
  • Hypothesis testing
  • Information spectrum
  • Mixed source
  • Optimum exponent

ASJC Scopus subject areas

  • General Physics and Astronomy


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