Related papers: On the empirical multilinear copula process for co…
We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general -…
An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not…
Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper demonstrates some difficulties with using copulas even for…
Tests for break points detection in the law of random vectors have been proposed in several papers. Nevertheless, they have often little powers for alternatives involving a change in the dependence between components of vectors. Specific…
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…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
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…
Working with so-called linkages allows to define a copula-based, $[0,1]$-valued multivariate dependence measure $\zeta^1(\boldsymbol{X},Y)$ quantifying the scale-invariant extent of dependence of a random variable $Y$ on a $d$-dimensional…
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…
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…
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…
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…
We propose a model for unbalanced longitudinal data, where the univariate margins can be selected arbitrarily and the dependence structure is described with the help of a D-vine copula. We show that our approach is an extremely flexible…
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…
Classical and more recent tests for detecting distributional changes in multivariate time series often lack power against alternatives that involve changes in the cross-sectional dependence structure. To be able to detect such changes…
The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on…
Probability density estimation from observed data constitutes a central task in statistics. In this brief, we focus on the problem of estimating the copula density associated to any observed data, as it fully describes the dependence…
Quantitative studies in many fields involve the analysis of multivariate data of diverse types, including measurements that we may consider binary, ordinal and continuous. One approach to the analysis of such mixed data is to use a copula…
When scholars study joint distributions of multiple variables, copulas are useful. However, if the variables are not linearly correlated with each other yet are still not independent, most of conventional copulas are not up to the task.…
Copulas are essential tools in statistics and probability theory, enabling the study of the dependence structure between random variables independently of their marginal distributions. Among the various types of copulas, Ratio-Type Copulas…