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.

翻译：本文在分布不确定性条件下建立了有限样本与渐近极小极大鲁棒假设检验之间的形式化联系。研究表明，当有限样本极小极大鲁棒检验存在时，其必然与对应渐近极小大问题的解相一致。这一结论使得利用渐近理论解析推导有限样本极小极大鲁棒检验成为可能，从而绕过了启发式构造的需求。研究以总变差距离和带状模型作为代表性不确定性类别进行考察。针对每种情形，均以参数化形式推导出最不利分布及其对应的鲁棒似然比函数。在总变差情形中，新推导通过允许非对称鲁棒参数推广了早期结果。该理论同时系统阐释了先前启发式设计的内在机理。文中通过仿真实验对理论结果进行了验证。