{"title":"Nonparametric tests for combined location-scale and Lehmann alternatives using adaptive approach and max-type metric","authors":"","doi":"10.1007/s42952-024-00262-7","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>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.</p>","PeriodicalId":49992,"journal":{"name":"Journal of the Korean Statistical Society","volume":"11 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Statistical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s42952-024-00262-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
The Journal of the Korean Statistical Society publishes research articles that make original contributions to the theory and methodology of statistics and probability. It also welcomes papers on innovative applications of statistical methodology, as well as papers that give an overview of current topic of statistical research with judgements about promising directions for future work. The journal welcomes contributions from all countries.
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