Optimal Decision Rules for Composite Binary Hypothesis Testing under Neyman-Pearson Framework
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909621234434048 |
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| author | Song, Yanglei Dulek, Berkan Gezici, Sinan |
| author_facet | Song, Yanglei Dulek, Berkan Gezici, Sinan |
| contents | The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability measure, subject to a false-alarm constraint. It is shown that each power function can be realized by a generalized Bayes rule that maximizes an integrated rejection probability with respect to a finite signed measure. For a simple null hypothesis and a composite alternative, optimal single-threshold decision rules based on an appropriately weighted likelihood ratio are derived. The analysis is extended to composite null hypotheses, including both average and worst-case false-alarm constraints, resulting in modified optimal threshold rules. Special cases involving exponential family distributions and numerical examples are provided to illustrate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Decision Rules for Composite Binary Hypothesis Testing under Neyman-Pearson Framework Song, Yanglei Dulek, Berkan Gezici, Sinan Statistics Theory Information Theory The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability measure, subject to a false-alarm constraint. It is shown that each power function can be realized by a generalized Bayes rule that maximizes an integrated rejection probability with respect to a finite signed measure. For a simple null hypothesis and a composite alternative, optimal single-threshold decision rules based on an appropriately weighted likelihood ratio are derived. The analysis is extended to composite null hypotheses, including both average and worst-case false-alarm constraints, resulting in modified optimal threshold rules. Special cases involving exponential family distributions and numerical examples are provided to illustrate the theoretical results. |
| title | Optimal Decision Rules for Composite Binary Hypothesis Testing under Neyman-Pearson Framework |
| topic | Statistics Theory Information Theory |
| url | https://arxiv.org/abs/2505.17851 |