Related papers: W-transforms: Uniformity-preserving transformation…
We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…
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…
For general repeated measures designs the Wald-type statistic (WTS) is an asymptotically valid procedure allowing for unequal covariance matrices and possibly non-normal multivariate observations. The drawback of this procedure is the poor…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
We study various properties of $f$-divergences and Csisz\'ar indices between two probability distributions in very general setups for the convex function $f$ and for the probability distributions. We establish general structural properties…
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…
The bivariate copulas that describe the dependencies and partial dependencies of lagged variables in strictly stationary, first-order GARCH-type processes are investigated. It is shown that the copulas of symmetric GARCH processes are…
We present a multiparameter generalization of the St\"ackel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized St\"ackel transform preserves the Liouville…
The study of dependence between random variables is the core of theoretical and applied statistics. Static and dynamic copula models are useful for describing the dependence structure, which is fully encrypted in the copula probability…
In the present paper we extend the multiparameter coupling constant metamorphosis, also known as the generalized St\"ackel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This…
Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
This article introduces a method for adjusting macro-particle weights within a particle distribution while preserving statistical and physical properties. The method allows the weights of the new macro-particle distribution to be determined…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
We propose to construct copulas from the inversion of nonlinear state space models. These allow for new time series models that have the same serial dependence structure of a state space model, but with an arbitrary marginal distribution,…
Dependence modeling of multivariate count data has garnered significant attention in recent years. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of…
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…
We propose the extension of Fr\'{e}chet-Hoeffding copula bounds for circular data. The copula is a powerful tool for describing the dependency of random variables. In two dimensions, the Fr\'{e}chet-Hoeffding upper (lower) bound indicates…
A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The…
In this article we summarize and describe the recently found transforms for theories of connections modulo gauge transformations associated with compact gauge groups. Specifically, we put into a coherent picture the so-called loop…
We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it…