In the 1970s, Professor Robbins and his coauthors extended the Vile and Wald inequality in order to derive the fundamental theoretical results regarding likelihood ratio based sequential tests with power one. The law of the iterated logarithm confirms an optimal property of the power one tests. In parallel with Robbins's decision-making procedures, we propose and examine sequential empirical likelihood ratio (ELR) tests with power one. In this setting, we develop the nonparametric one- and two-sided ELR tests. It turns out that the proposed sequential ELR tests significantly outperform the classical nonparametric t-statistic-based counterparts in many scenarios based on different underlying data distributions.

中文翻译：

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幂一的经验似然比检验

在 1970 年代，Robbins 教授和他的合著者扩展了 Vile 和 Wald 不等式，以推导出关于基于似然比的序贯检验的基本理论结果。迭代对数定律证实了幂一测试的最佳属性。与 Robbins 的决策程序并行，我们提出并检验了具有幂一的序列经验似然比 (ELR) 检验。在这种情况下，我们开发了非参数单边和双边 ELR 检验。事实证明，在基于不同基础数据分布的许多场景中，所提出的顺序 ELR 测试显着优于基于经典非参数 t 统计量的对应测试。