Related papers: Copula-like inference for discrete bivariate distr…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
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…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
The need for a method to construct multidimensional distribution function is increasing recently, in the era of huge multiwavelength surveys. We have proposed a systematic method to build a bivariate luminosity or mass function of galaxies…
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…
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…
A new family of distributions indexed by the class of matrix variate contoured elliptically distribution is proposed as an extension of some bimatrix variate distributions. The termed \emph{multimatrix variate distributions} open new…
The assessment of regression models with discrete outcomes is challenging and has many fundamental issues. With discrete outcomes, standard regression model assessment tools such as Pearson and deviance residuals do not follow the…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
Consider a uniform variate on the unit upper-half sphere of dimension $d$. It is known that the straight-line projection through the center of the unit sphere onto the plane above it distributes this variate according to a $d$-dimensional…
In some areas of knowledge there are data representing directions restricted to a specific range of values. Consequently, it is useful to have models for describing variables defined in subsets of the k-dimensional unit sphere. This need…
A copula of continuous random variables $X$ and $Y$ is called an \emph{implicit dependence copula} if there exist functions $\alpha$ and $\beta$ such that $\alpha(X) = \beta(Y)$ almost surely, which is equivalent to $C$ being factorizable…
Christoffel polynomials are classical tools from approximation theory. They can be used to estimate the (compact) support of a measure $\mu$ on $\mathbb{R}^d$ based on its low-degree moments. Recently, they have been applied to problems in…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…
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…
Using some extensions of a theorem of Heppes on finitely supported discrete probability measures, we address the problems of classification and testing based on projections. In particular, when the support of the distributions is known in…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to…