Related papers: The empirical discrete copula process

After reviewing a large body of literature on the modeling of bivariate discrete distributions with finite support, \cite{Gee20} made a compelling case for the use of $I$-projections in the sense of \cite{Csi75} as a sound way to attempt to…

Continuation refers to the operation by which the cumulative distribution function of a discontinuous random vector is made continuous through multilinear interpolation. The copula that results from the application of this technique to the…

In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their…

The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions…

In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. We introduce the concept of multivariate discrete copulas, discuss their equivalence to…

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case…

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…

Multi-dimensional distributions whose marginal distributions are uniform are called copulas. Among them, the one that satisfies given constraints on expectation and is closest to the independent distribution in the sense of Kullback-Leibler…

When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…

The authors transpose a discrete notion of indetermination coupling in the case of continuous probabilities. They show that this coupling, expressed on densities, cannot be captured by a specific copula which acts on cumulative distribution…

The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…

Modeling of high order multivariate probability distribution is a difficult problem which occurs in many fields. Copula approach is a good choice for this purpose, but the curse of dimensionality still remains a problem. In this paper we…

The continuous extension of a discrete random variable is amongst the computational methods used for estimation of multivariate normal copula-based models with discrete margins. Its advantage is that the likelihood can be derived…

In this paper, we study the identifiability and the estimation of the parameters of a copula-based multivariate model when the margins are unknown and are arbitrary, meaning that they can be continuous, discrete, or mixtures of continuous…

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…

Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…

Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…

In this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal: I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48--66. The main tools we…

The minimum information copula principle initially suggested in \cite{MeeBed97} is a maximum entropy-like approach for finding the least informative copula, if it exists, that satisfies a certain number of expectation constraints specified…

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…