Related papers: Copula Measures and Sklar's Theorem in Arbitrary D…
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…
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…
Copulas are a powerful tool to model dependence between the components of a random vector. One well-known class of copulas when working in two dimensions is the Farlie-GumbelMorgenstern (FGM) copula since their simple analytic shape enables…
The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…
A factor copula model is proposed in which factors are either simulable or estimable from exogenous information. Point estimation and inference are based on a simulated methods of moments (SMM) approach with non-overlapping simulation…
Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…
When modeling the distribution of a multivariate continuous random vector using the so-called \emph{copula approach}, it is not uncommon to have ties in the coordinate samples of the available data because of rounding or lack of measurement…
Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
This paper lays out a principled approach to compare copula forecasts via strictly consistent scores. We first establish the negative result that, in general, copulas fail to be elicitable, implying that copula predictions cannot sensibly…
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…
We exploit Gaussian copulas to specify a class of multivariate circular distributions and obtain parametric models for the analysis of correlated circular data. This approach provides a straightforward extension of traditional multivariate…
Explicit functional forms for the generator derivatives of well-known one-parameter Archimedean copulas are derived. These derivatives are essential for likelihood inference as they appear in the copula density, conditional distribution…
This paper focuses on a generalization of the *-product called $\mathbf{C}$-product. This product, first introduced by Durante, Klement and Quesada-Molina, was used to characterize classes of compatible copulas. The $\mathbf{C}$-product of…
According to the Dudley-Wichura extension of the Skorohod representation theorem, convergence in distribution to a limit in a separable set is equivalent to the existence of a coupling with elements converging a.s. in the metric. A density…
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp…
We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…