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We propose an approach to construct a new family of generalized Farlie-Gumbel-Morgenstern (GFGM) copulas that naturally scales to high dimensions. A GFGM copula can model moderate positive and negative dependence, cover different types of…
Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our…
Instance-wise feature selection and ranking methods can achieve a good selection of task-friendly features for each sample in the context of neural networks. However, existing approaches that assume feature subsets to be independent are…
This paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous components. The particular cases of independent components and homogeneous components are also considered. We model the…
Factor models are a parsimonious way to explain the dependence of variables using several latent variables. In Gaussian 1-factor and structural factor models (such as bi-factor, oblique factor) and their factor copula counterparts, factor…
The mean-variance portfolio model, based on the risk-return trade-off for optimal asset allocation, remains foundational in portfolio optimization. However, its reliance on restrictive assumptions about asset return distributions limits its…
Handling highly dependent data is crucial in clinical trials, particularly in fields related to ophthalmology. Incorrectly specifying the dependency structure can lead to biased inferences. Traditionally, models rely on three fixed…
Uncertain information on input parameters of reliability models is usually modeled by considering these parameters as random, and described by marginal distributions and a dependence structure of these variables. In numerous real-world…
A novel positive dependence property is introduced, called positive measure inducing (PMI for short), being fulfilled by numerous copula classes, including Gaussian, Fr\'echet, Farlie-Gumbel-Morgenstern and Frank copulas; it is conjectured…
Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature…
In this paper we study nonparametric estimators of copulas and copula densities. We first focus our study on a density copula estimator based on a polynomial orthogonal projection of the joint density. A new copula estimator is then…
Asymmetry is an inherent property of bivariate associations and therefore must not be ignored. The currently applicable dependence measures mask the potential asymmetry of the underlying dependence structure by implicitly assuming that…
We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail…
In actuarial research, a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking, and capital…
This work provides a study of parameter estimators based on functions of Markov chains generated by some perturbations of the independence copula. We provide asymptotic distributions of maximum likelihood estimators and confidence intervals…
Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
In this paper, we compare two numerical methods for approximating the probability that the sum of dependent regularly varying random variables exceeds a high threshold under Archimedean copula models. The first method is based on…
Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…
In conditional copula models, the copula parameter is deterministically linked to a covariate via the calibration function. The latter is of central interest for inference and is usually estimated nonparametrically. However, when a…