Independence tests based on the shape of the Standard Young Tableau

Jesús Enrique García (), Verónica Andrea González-López () and María Magdalena Kcala Álvaro ()
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Jesús Enrique García: University of Campinas
Verónica Andrea González-López: University of Campinas
María Magdalena Kcala Álvaro: University of Campinas

Computational Statistics, 2025, vol. 40, issue 9, No 7, 5043-5074

Abstract: Abstract 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.

Keywords: Permutations; Non-parametric tests; Jackknife; Simulations (search for similar items in EconPapers)
JEL-codes: C12 C14 C15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01597-9

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