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Entropy 2016, 18(8), 400;

Optimal Noise Benefit in Composite Hypothesis Testing under Different Criteria

College of Communication Engineering, Chongqing University, Chongqing 400044, China
Chongqing Key Lab of Mobile Communications Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Author to whom correspondence should be addressed.
Academic Editors: Julio Stern, Adriano Polpo and Kevin H. Knuth
Received: 30 May 2016 / Revised: 14 August 2016 / Accepted: 16 August 2016 / Published: 19 August 2016
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
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The detectability for a noise-enhanced composite hypothesis testing problem according to different criteria is studied. In this work, the noise-enhanced detection problem is formulated as a noise-enhanced classical Neyman–Pearson (NP), Max–min, or restricted NP problem when the prior information is completely known, completely unknown, or partially known, respectively. Next, the detection performances are compared and the feasible range of the constraint on the minimum detection probability is discussed. Under certain conditions, the noise-enhanced restricted NP problem is equivalent to a noise-enhanced classical NP problem with modified prior distribution. Furthermore, the corresponding theorems and algorithms are given to search the optimal additive noise in the restricted NP framework. In addition, the relationship between the optimal noise-enhanced average detection probability and the constraint on the minimum detection probability is explored. Finally, numerical examples and simulations are provided to illustrate the theoretical results. View Full-Text
Keywords: additive noise; composite hypothesis testing; restricted Neyman–Pearson (NP) additive noise; composite hypothesis testing; restricted Neyman–Pearson (NP)

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Liu, S.; Yang, T.; Tang, M.; Liu, H.; Zhang, K.; Zhang, X. Optimal Noise Benefit in Composite Hypothesis Testing under Different Criteria. Entropy 2016, 18, 400.

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