arXiv subjects

Enrique de Amo

Publications and source records attributed to Enrique de Amo.

6 recordsLinked to original sources

arXiv2026

The W-footrule coefficient: A copula-based measure of countermonotonicity

We introduce the $W$-footrule coefficient $Φ_C$, a copula-based coefficient of negative association defined as the $L^1$-distance to the countermonotonic copula $W$. We prove that Gini's gamma admits the decomposition $γ_C = \frac{2}{3}(φ_C+Φ_C)$, linking it to Spearman's footrule $φ_C$. A rank-based estimator is introduced, with its strong consistency and asymptotic normality established via the functional delta method. Monte Carlo simulations confirm the estimator's finite-sample validity and its sensitivity to negative dependence structures.

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arXiv2026

Convex lineability in copula and quasi-copula sets

In this paper, we investigate several subsets of $n$-copulas and $n$-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain extremely large algebraic structures, namely linearly independent sets of cardinality of the continuum whose convex hull, and in some cases a closed convex linearly independent subset, remain entirely inside the class under study. These include the families of asymmetric copulas, copulas with maximal asymmetric measure, and proper $n$-quasi-copulas, among others. In contrast, for several other natural classes of copulas we show that (maximal) convex lineability holds while convex spaceability remains an open problem.

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arXiv2026

Directional footrule-coefficients

Rank-based dependence measures such as Spearman's footrule are robust and invariant, but they often fail to capture directional or asymmetric dependence in multivariate settings. This paper introduces a new family of directional Spearman's footrule coefficients for multivariate data, defined within the copula framework to clearly separate marginal behavior from dependence structure. We establish their main theoretical properties, showing full consistency with the classical footrule, including behavior under independence and extreme dependence, as well as symmetry and reflection properties. Nonparametric rank-based estimators are proposed and their asymptotic consistency is discussed. Explicit expressions for several known families of copulas illustrate the ability of the proposed coefficients to detect directional dependence patterns undetected by classical measures.

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arXiv2025

Directional $ρ$-coefficients

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.

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arXiv2025

Total positivity and dependence of order statistics

In this comprehensive study, we delve deeply into the concept of multivariate total positivity, defining it in accordance with a direction. We rigorously explore numerous salient properties, shedding light on the nuances that characterize this notion. Furthermore, our research extends to establishing distinct forms of dependence among the order statistics of a sample from a distribution function. Our analysis aims to provide a nuanced understanding of the interrelationships within multivariate total positivity and its implications for statistical analysis and probability theory.

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arXiv2025

Modeling directional monotonicity with copulas

The purpose of this paper is to characterize the concept of monotonicity according to a direction related to a set of n random variables in terms of its associated n-copula C. We start establishing relationships in the bivariate and trivariate cases, which help to understand the extension to the multivariate case. Examples of copulas in all the studied cases are provided.

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