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Copulas are popular as models for multivariate dependence because they allow the marginal densities and the joint dependence to be modeled separately. However, they usually require that the transformation from uniform marginals to the…
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…
We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
The increasing use of vine copulas in high-dimensional settings, where the number of parameters is often of the same order as the sample size, calls for asymptotic theory beyond the traditional fixed-$p$, large-$n$ framework. We establish…
An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em…
This paper introduces a new class of Cox models for dependent bivariate data. The impact of the covariate on the dependence of the variables is captured through the modification of their copula. Various classes of well known copulas are…
We introduce the notion of a bivariate random discrete copula on an equidistant mesh and explore its stochastic properties. A random discrete copula is a discrete random field, hence, its value at a given point on the mesh is a random…
We address an important yet challenging problem - modeling high-dimensional dependencies across multivariates such as financial indicators in heterogeneous markets. In reality, a market couples and influences others over time, and the…
This paper considers the problem of invoking auxiliary, unobservable variables to facilitate the structuring of causal tree models for a given set of continuous variables. Paralleling the treatment of bi-valued variables in [Pearl 1986], we…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the…
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…
Normal copula with a correlation coefficient between $-1$ and $1$ is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H\"usler and…
The continuous dependence of solutions to certain (non-autonomous, partial, integro-differential-algebraic, evolutionary) equations on the coefficients is addressed. We give criteria that guarantee that convergence of the coefficients in…
This paper provides a characterization of all possible dependency structures between two stochastically ordered random variables. The answer is given in terms of copulas that are compatible with the stochastic order and the marginal…
This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we…
Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this…
The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…
Normalizing flows, a popular class of deep generative models, often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes,…