Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/316978 
Year of Publication: 
2024
Citation: 
[Journal:] Journal of the Korean Statistical Society [ISSN:] 2005-2863 [Volume:] 53 [Issue:] 3 [Publisher:] Springer Nature Singapore [Place:] Singapore [Year:] 2024 [Pages:] 666-703
Publisher: 
Springer Nature Singapore, Singapore
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.
Subjects: 
Adaptive test
Asymptotic power
Maximum test
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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