Directional $ρ$-coefficients

Fuente: arXiv
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Hauptverfasser: de Amo, Enrique, García-Fernández, David, Úbeda-Flores, Manuel
Format: Preprint
Veröffentlicht: 2025
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author de Amo, Enrique
García-Fernández, David
Úbeda-Flores, Manuel
author_facet de Amo, Enrique
García-Fernández, David
Úbeda-Flores, Manuel
contents In this paper we obtain advances for the concept of directional $ρ$-coefficients, originally defined for the trivariate case in [Nelsen, R.B., Úbeda-Flores, M. (2011). Directional dependence in multivariate distributions. Ann. Inst. Stat. Math 64, 677-685] by extending it to encompass arbitrary dimensions and directions in multivariate space. We provide a generalized definition and establish its fundamental properties. Moreover, we resolve a conjecture from the aforementioned work by proving a more general result applicable to any dimension, correcting a result in [García, J.E., González-López, V.A., Nelsen, R.B. (2013). A new index to measure positive dependence in trivariate distributions. J. Multivariate Anal. 115, 481-495] an erratum in the current literature. Our findings contribute to a deeper understanding of multivariate dependence and association, offering novel tools for detecting directional dependencies in high-dimensional settings. Finally, we introduce nonparametric estimators, based on ranks, for estimating directional $ρ$-coefficients from a sample.
format Preprint
id arxiv_https___arxiv_org_abs_2505_22206
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Directional $ρ$-coefficients
de Amo, Enrique
García-Fernández, David
Úbeda-Flores, Manuel
Statistics Theory
62H05, 62H12
In this paper we obtain advances for the concept of directional $ρ$-coefficients, originally defined for the trivariate case in [Nelsen, R.B., Úbeda-Flores, M. (2011). Directional dependence in multivariate distributions. Ann. Inst. Stat. Math 64, 677-685] by extending it to encompass arbitrary dimensions and directions in multivariate space. We provide a generalized definition and establish its fundamental properties. Moreover, we resolve a conjecture from the aforementioned work by proving a more general result applicable to any dimension, correcting a result in [García, J.E., González-López, V.A., Nelsen, R.B. (2013). A new index to measure positive dependence in trivariate distributions. J. Multivariate Anal. 115, 481-495] an erratum in the current literature. Our findings contribute to a deeper understanding of multivariate dependence and association, offering novel tools for detecting directional dependencies in high-dimensional settings. Finally, we introduce nonparametric estimators, based on ranks, for estimating directional $ρ$-coefficients from a sample.
title Directional $ρ$-coefficients
topic Statistics Theory
62H05, 62H12
url https://arxiv.org/abs/2505.22206