Related papers: Copula Index for Detecting Dependence and Monotoni…
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
Analysing dependent risks is an important task for insurance companies. A dependency is reflected in the fact that information about one random variable provides information about the likely distribution of values of another random…
In statistics and machine learning, detecting dependencies in datasets is a central challenge. We propose a novel neural network model for supervised graph structure learning, i.e., the process of learning a mapping between observational…
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…
Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena…
We construct the COpula Recursive Tree (CORT) estimator: a flexible, consistent, piecewise linear estimator of a copula, leveraging the patchwork copula formalization and various piecewise constant density estimators. While the patchwork…
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…
This paper proposes a new semi-parametric identification and estimation approach to multinomial choice models in a panel data setting with individual fixed effects. Our approach is based on cyclic monotonicity, which is a defining feature…
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…
This is the monograph on the theory and applications of copula entropy (CE). This book first introduces the theory of CE, including its background, definition, theorems, properties, and estimation methods. The theoretical applications of CE…
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…
We propose a novel framework that harnesses the power of generative artificial intelligence and copula-based modeling to address two critical challenges in multivariate time-series analysis: delivering accurate predictions and enabling…
Background: Current mathematical quantification methods for beam symmetry are highly sensitive to noise, especially in beam profiles with significant variation. Purpose: This study evaluates the accuracy of standard radiotherapy beam…
We propose and demonstrate a joint model of anatomical shapes, image features and clinical indicators for statistical shape modeling and medical image analysis. The key idea is to employ a copula model to separate the joint dependency…
Dette, Siburg, and Stoimenov (2013) introduced a copula-based measure of dependence, which implies independence if it vanishes and is equal to 1 if one variable is a measurable function of the other. For continuous distributions, the…
Most common parametric families of copulas are totally ordered, and in many cases they are also positively or negatively regression dependent and therefore they lead to monotone regression functions, which makes them not suitable for…
Discovering associations is of central importance in scientific practices. Currently, most researches consider only linear association measured by correlation coefficient, which has its theoretical limitations. In this paper, we propose a…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
We propose a score test for dependence predictability in conditional copulas that is robust to temporal instabilities. Our semiparametric procedure accommodates flexible dynamics in the marginal processes and remains agnostic about the…
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…