A Multivariate Quantile Based on Kendall Ordering

• Main Author: Garcin , Matthieu
• Publication Date: 2023
• Other Authors: Guégan , Dominique, Hassani , Bertrand
• Format: Article
• Language: eng
• Source: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Download full: https://doi.org/10.57805/revstat.v21i1.397
• topic: multivariate quantile; copula; Archimedean copula; Kendall distribution; orthant quantile

We introduce the Kendall multivariate quantiles, which are a transformation of orthant quantiles by the Kendall function. Each quantile is then a set of vectors with some advantageous properties, compared to the standard orthant quantile: i/ it in[1]duces a total order, ii/ the probability level of the quantile is consistent with the probability measure of the set of the dominated vectors, iii/ the multivariate quantiles based on the distribution function or on the survival function have vectors in common which conciliate both upper- and lower-orthant approaches. Definition and properties of the Kendall multivariate quantiles are illustrated using Archimedean copulas.