Nonparametric tests for combined location-scale and Lehmann alternatives using adaptive approach and max-type metric

Pub Date : 2024-04-02 DOI:10.1007/s42952-024-00262-7

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Abstract

The paper deals with the classical two-sample problem for the combined location-scale and Lehmann alternatives, known as the versatile alternative. Recently, a combination of the square of the standardized Wilcoxon, the standardized Ansari–Bradley and the standardized Anti-Savage statistics based on the Euclidean distance has been proposed. The Anti-Savage test is the locally most powerful rank test for the right-skewed Gumbel distribution. Furthermore, the Savage test is the locally most powerful linear rank test for the left-skewed Gumbel distribution. Then, a test statistic combining the Wilcoxon, the Ansari–Bradley, and Savage statistics is proposed. The limiting distribution of the proposed statistic is derived under the null and the alternative hypotheses. In addition, the asymptotic power of the suggested statistic is investigated. Moreover, an adaptive test is proposed based on a selection rule. We compare the power performance against various fixed alternatives using Monte Carlo. The proposed test statistic displays outstanding performance in certain situations. An illustration of the proposed test statistic is presented to explain a biomedical experiment. Finally, we offer some concluding remarks.

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利用自适应方法和最大类型度量对位置尺度和莱曼综合替代方案进行非参数检验

摘要本文论述了位置标度和莱曼替代方案（称为多用途替代方案）组合的经典双样本问题。最近，有人提出了基于欧氏距离的标准化 Wilcoxon、标准化 Ansari-Bradley 和标准化 Anti-Savage 统计量的平方组合。反萨维奇检验是右偏 Gumbel 分布的局部最强秩检验。此外，对于左偏 Gumbel 分布，Savage 检验是局部最强的线性秩检验。然后，提出了一种结合 Wilcoxon、Ansari-Bradley 和 Savage 统计量的检验统计量。在零假设和备择假设下，得出了所提统计量的极限分布。此外，还研究了建议统计量的渐近功率。此外，还提出了一种基于选择规则的自适应检验。我们使用蒙特卡罗方法比较了各种固定替代方案的功率性能。所提出的检验统计量在某些情况下表现突出。我们以一个生物医学实验为例，对所提出的检验统计量进行了说明。最后，我们提出一些结束语。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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