Directional $ρ$-coefficients
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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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 |