Jesus Garcia (IMECC-UNICAMP)

Title: Testing for Copula Distribution Equality Using Young Diagrams

We present a methodology based on Young diagrams to assess the equality of copula distributions between two continuous bi-variate samples. Given samples of sizes n and m from continuous bi-variate distributions F and G respectively, we construct permutations from their scatter plots (see [1], [2]). For each permutation, we compute its corresponding Young diagram whose shape is linked to the underlying copula distribution of the bi-variate data (see [3]). This relationship forms the foundation for a test of copula distribution equality (joint work with V. Gonzalez-Lopez).

References:

[1] Garcia J.E.; Gonzalez-Lopez, V.A. Independence tests for continuous random variables based on the longest increasing subsequence. Journal of Multivariate Analysis, 2014, 127,

126-146 (Doi:10.1016/j.jmva.2014.02.010)

[2] Garcia, J.E.; Gonzalez-Lopez, V.A. Random Permutations, Non-Decreasing Subse-quences and Statistical Independence. Symmetry 2020, 12, 1415 (Doi: 10.3390/sym12091415)

[3] Garcia JE, Gonzalez-Lopez VA, Alvaro MMK. Independence tests based on the shape of the Standard Young Tableau. Computational Statistics. 2025. https://doi.org/10.1007/s00180-024-01597-9