<p>The multisample problem is a fundamental research topic across various fields, including biomedical studies and quality control in manufacturing. The Kruskal–Wallis test is widely employed for assessing differences in location parameters among multiple samples. However, real-world data rarely exhibit variations solely in location parameters, necessitating alternative approaches. The multisample Anderson–Darling test is commonly used to assess the equality of entire distributions rather than just location shifts. In financial and hydrological applications, the behavior of the upper or lower tail of a distribution is often of greater importance than central tendencies. In this study, we propose a novel multisample test statistic that is particularly sensitive to differences in the tails of distributions. We derive the limiting distribution of the proposed test statistic under the null hypothesis and develop an approximation method for its distribution function. The accuracy of this approximation is evaluated through simulation studies. Furthermore, we compare the power of the proposed test statistic against existing test statistics. The effectiveness of our approach is demonstrated through applications to real datasets, and we conclude with a discussion of our findings and potential directions for future research.</p>

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Multisample Version of the Modified Anderson–Darling Statistic

  • Ayaka Tamaki,
  • Hidetoshi Murakami,
  • Masato Kitani

摘要

The multisample problem is a fundamental research topic across various fields, including biomedical studies and quality control in manufacturing. The Kruskal–Wallis test is widely employed for assessing differences in location parameters among multiple samples. However, real-world data rarely exhibit variations solely in location parameters, necessitating alternative approaches. The multisample Anderson–Darling test is commonly used to assess the equality of entire distributions rather than just location shifts. In financial and hydrological applications, the behavior of the upper or lower tail of a distribution is often of greater importance than central tendencies. In this study, we propose a novel multisample test statistic that is particularly sensitive to differences in the tails of distributions. We derive the limiting distribution of the proposed test statistic under the null hypothesis and develop an approximation method for its distribution function. The accuracy of this approximation is evaluated through simulation studies. Furthermore, we compare the power of the proposed test statistic against existing test statistics. The effectiveness of our approach is demonstrated through applications to real datasets, and we conclude with a discussion of our findings and potential directions for future research.