First- and second-order hypothesis testing for mixed memoryless sources with general mixture

Te Sun Han; Ryo Nomura

doi:10.1109/ISIT.2017.8006503

First- and second-order hypothesis testing for mixed memoryless sources with general mixture

Te Sun Han, Ryo Nomura

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

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-exponent in the case where the null hypothesis and the 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. We address the first-order ϵ-optimum exponent in this setting.

Original language	English
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	126-130
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8006503
Publication status	Published - 2017 Aug 9
Externally published	Yes
Event	2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: 2017 Jun 25 → 2017 Jun 30

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Other

Other	2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/Territory	Germany
City	Aachen
Period	17/6/25 → 17/6/30

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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10.1109/ISIT.2017.8006503

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Han, T. S., & Nomura, R. (2017). First- and second-order hypothesis testing for mixed memoryless sources with general mixture. In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 126-130). Article 8006503 (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006503

First- and second-order hypothesis testing for mixed memoryless sources with general mixture. / Han, Te Sun; Nomura, Ryo.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 126-130 8006503 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Han, TS & Nomura, R 2017, First- and second-order hypothesis testing for mixed memoryless sources with general mixture. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006503, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 126-130, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 17/6/25. https://doi.org/10.1109/ISIT.2017.8006503

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abstract = "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-exponent in the case where the null hypothesis and the 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. We address the first-order ϵ-optimum exponent in this setting.",

author = "Han, {Te Sun} and Ryo Nomura",

note = "Funding Information: The second author with this work was supported in part by JSPS KAKENHI Grant Number 26420371.; 2017 IEEE International Symposium on Information Theory, ISIT 2017 ; Conference date: 25-06-2017 Through 30-06-2017",

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doi = "10.1109/ISIT.2017.8006503",

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AB - 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-exponent in the case where the null hypothesis and the 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. We address the first-order ϵ-optimum exponent in this setting.

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First- and second-order hypothesis testing for mixed memoryless sources with general mixture

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