Scholarlink

<p>We introduce a novel family of tests designed to assess the hypothesis of independence between two continuous random variables, <i>X</i> and <i>Y</i>. This test family is constructed around a new concept presented here-the shape vector derived from the Standard Young Tableau, obtained through the application of an algorithm [introduced by Schensted (Canad J Math 13:179–191, 1961. <a href="https://doi.org/10.4153/CJM-1961-015-3">https://doi.org/10.4153/CJM-1961-015-3</a>)] to the permutation mapping the ranks of <i>X</i> observations onto the ranks of <i>Y</i> observations. We present diverse statistics based on the shape vector from the Standard Young Tableau. The empirical distributions associated with this innovative family of statistics are established through simulations, supported by various procedures detailed in this paper. The efficacy of dependence detection exhibited by this new test family is demonstrated through simulated scenarios and real datasets. Notably, the proposed family demonstrates a capability to detect dependence in situations where traditional tests of independence, such as those based on association or correlation coefficients, falter.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Independence tests based on the shape of the Standard Young Tableau

  • 期刊论文

  • 发表日期：

    2025年1月17日

查看全文
  • Jesús Enrique García,
  • Verónica Andrea González-López,
  • María Magdalena Kcala Álvaro

摘要

We introduce a novel family of tests designed to assess the hypothesis of independence between two continuous random variables, X and Y. This test family is constructed around a new concept presented here-the shape vector derived from the Standard Young Tableau, obtained through the application of an algorithm [introduced by Schensted (Canad J Math 13:179–191, 1961. https://doi.org/10.4153/CJM-1961-015-3)] to the permutation mapping the ranks of X observations onto the ranks of Y observations. We present diverse statistics based on the shape vector from the Standard Young Tableau. The empirical distributions associated with this innovative family of statistics are established through simulations, supported by various procedures detailed in this paper. The efficacy of dependence detection exhibited by this new test family is demonstrated through simulated scenarios and real datasets. Notably, the proposed family demonstrates a capability to detect dependence in situations where traditional tests of independence, such as those based on association or correlation coefficients, falter.