Related papers: A novel characterization and new simple tests of m…
Copulas are now frequently used to construct or estimate multivariate distributions because of their ability to take into account the multivariate dependence of the different variables while separately specifying marginal distributions.…
In this paper we review Bernstein and grid-type copulas for arbitrary dimensions and general grid resolutions in connection with discrete random vectors possessing uniform margins. We further suggest a pragmatic way to fit the dependence…
It is well known and readily seen that the maximum of $n$ independent and uniformly on $[0,1]$ distributed random variables, suitably standardised, converges in total variation distance, as $n$ increases, to the standard negative…
We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression…
Handling highly dependent data is crucial in clinical trials, particularly in fields related to ophthalmology. Incorrectly specifying the dependency structure can lead to biased inferences. Traditionally, models rely on three fixed…
Copulas provide an attractive approach for constructing multivariate distributions with flexible marginal distributions and different forms of dependences. Of particular importance in many areas is the possibility of explicitly forecasting…
We study a new measure of codependency in the second moment of a continuous-time multivariate asset price process, which we name the realized copula of volatility. The statistic is based on local volatility estimates constructed from…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
We are concerned with the detection of associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all…
In this paper we construct the new coefficient which allows to measure quantitatively the independence of the two discrete random variables. The new inequalities for the matrices with non-negative elements are found
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…
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…
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…
In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
Some problems of statistics can be reduced to extremal problems of minimizing functionals of smooth functions defined on the cube $[0,1]^m$, $m\geq 2$. In this paper, we study a class of extremal problems that is closely connected to the…
Change point detection is a typical task that aim to find changes in time series and can be tackled with two-sample test. Copula Entropy is a mathematical concept for measuring statistical independence and a two-sample test based on it was…
We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for…
Statistical independence and conditional independence are two fundamental concepts in statistics and machine learning. Copula Entropy is a mathematical concept defined by Ma and Sun for multivariate statistical independence measuring and…
Due to the lack of a canonical ordering in ${\mathbb R}^d$ for $d>1$, defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been shown to offer a…