Paper
From Asymptotic to Finite-Sample Minimax Robust Hypothesis Testing
Authors
Gökhan Gül
Abstract
This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with the solution of the corresponding asymptotic minimax problem. This result enables the analytical derivation of finite-sample minimax robust tests using asymptotic theory, bypassing the need for heuristic constructions. The total variation distance and band model are examined as representative uncertainty classes. For each, the least favorable distributions and corresponding robust likelihood ratio functions are derived in parametric form. In the total variation case, the new derivation generalizes earlier results by allowing unequal robustness parameters. The theory also explains and systematizes previously heuristic designs. Simulations are provided to illustrate the theoretical results.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.19803v1</id>\n <title>From Asymptotic to Finite-Sample Minimax Robust Hypothesis Testing</title>\n <updated>2026-02-23T12:59:22Z</updated>\n <link href='https://arxiv.org/abs/2602.19803v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.19803v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with the solution of the corresponding asymptotic minimax problem. This result enables the analytical derivation of finite-sample minimax robust tests using asymptotic theory, bypassing the need for heuristic constructions. The total variation distance and band model are examined as representative uncertainty classes. For each, the least favorable distributions and corresponding robust likelihood ratio functions are derived in parametric form. In the total variation case, the new derivation generalizes earlier results by allowing unequal robustness parameters. The theory also explains and systematizes previously heuristic designs. Simulations are provided to illustrate the theoretical results.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.ST'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.IT'/>\n <published>2026-02-23T12:59:22Z</published>\n <arxiv:comment>40 pages, 6 figures. Submitted to IEEE Transactions on Information Theory</arxiv:comment>\n <arxiv:primary_category term='math.ST'/>\n <author>\n <name>Gökhan Gül</name>\n </author>\n </entry>"
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