Volume 6, 2023
Statistical Inference in Markov Processes and Copula Models
|Number of page(s)||7|
|Section||Mathematics - Applied Mathematics|
|Published online||11 May 2023|
Statistical dependence and shape of Young tableau
Department of Statistics, University of Campinas, Sergio Buarque de Holanda, 651, Campinas, SP CEP: 13083-859, Brazil
* Corresponding author: email@example.com
Accepted: 27 March 2023
Given two continuous random variables, X and Y, we study the relationship between their statistical dependence and the Young tableau of the permutation defined from the graph of a bivariate sample coming from (X, Y). From a sample of size n of (X, Y), we identify the Young tableau of the permutation which maps the ranks of the X observations on the ranks of the Y observations. Procedures to detect statistical dependence between pairs of random variables, based on statistics calculated on the permutation defined by the graph of a bivariate sample have been developed, see García and González-López (2020) [Symmetry 12, 9, 1415. https://doi.org/10.3390/sym12091415] and García and González-López (2014) [J Multivar Anal 127, 126–146. https://doi.org/10.1016/j.jmva.2014.02.010]. In those papers, the information used is the length of the longest increasing (decreasing) subsequence, identified as the first line (the first column) of the Young tableau of the permutation. In this paper, we expose the information captured by the shape of the Young tableau of the permutation.
Key words: Permutation / Young tableau / Statistical dependence
© J.E. García et al., Published by EDP Sciences, 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.