First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources
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 -opt...
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MDPI AG
2018-03-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/3/174 |
| _version_ | 1811278881796128768 |
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| author | Te Sun Han Ryo Nomura |
| author_facet | Te Sun Han Ryo Nomura |
| author_sort | Te Sun Han |
| collection | DOAJ |
| description | 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. |
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| id | doaj.art-9f539b50bbfc4b8db2f5383dfa93f05b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T00:43:31Z |
| publishDate | 2018-03-01 |
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| spelling | doaj.art-9f539b50bbfc4b8db2f5383dfa93f05b2022-12-22T03:10:04ZengMDPI AGEntropy1099-43002018-03-0120317410.3390/e20030174e20030174First- and Second-Order Hypothesis Testing for Mixed Memoryless SourcesTe Sun Han0Ryo Nomura1National Institute of Information and Communications Technology (NICT), Tokyo 184-8795, JapanSchool of Network and Information, Senshu University, Kanagawa 214-8580, JapanThe 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.http://www.mdpi.com/1099-4300/20/3/174general sourcehypothesis testinginformation spectrummixed sourceoptimum exponent |
| spellingShingle | Te Sun Han Ryo Nomura First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources Entropy general source hypothesis testing information spectrum mixed source optimum exponent |
| title | First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources |
| title_full | First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources |
| title_fullStr | First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources |
| title_full_unstemmed | First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources |
| title_short | First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources |
| title_sort | first and second order hypothesis testing for mixed memoryless sources |
| topic | general source hypothesis testing information spectrum mixed source optimum exponent |
| url | http://www.mdpi.com/1099-4300/20/3/174 |
| work_keys_str_mv | AT tesunhan firstandsecondorderhypothesistestingformixedmemorylesssources AT ryonomura firstandsecondorderhypothesistestingformixedmemorylesssources |