Related papers: Shaping tail dependencies by nesting box copulas
We propose a new family of copulas generalizing the Farlie-Gumbel-Morgenstern family and generated by two univariate functions. The main feature of this family is to permit the modeling of high positive dependence. In particular, it is…
We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on…
We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…
Optimum experimental design theory has recently been extended for parameter estimation in copula models. However, the choice of the correct dependence structure still requires wider analyses. In this work the issue of copula selection is…
We consider a metapopulation version of the Schelling model of segregation over several complex networks and lattice. We show that the segregation process is topology independent and hence it is intrinsic to the individual tolerance. The…
We construct a family of monotone and convex $C^1$ integro cubic splines under a strictly convex position of the dataset. Then, we find an optimal spline by considering its approximation properties. Finally, we give some examples to…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is…
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
In this paper, we develop a comprehensive asymptotic and bootstrap theory for checkerboard-based estimation of lower and upper tail copulas under unknown marginal distributions. The estimator is constructed via local bilinear (checkerboard)…
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…
We develop a novel characterization of extremal dependence between two cortical regions of the brain when its signals display extremely large amplitudes. We show that connectivity in the tails of the distribution reveals unique features of…
The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having…
The assembly of colloids in nematic liquid crystals via topological defects has been extensively studied for spherical particles, and investigations of other colloid shapes have revealed a wide array of new assembly behaviors. We show,…
We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals,…
This paper introduces vector copulas associated with multivariate distributions with given multivariate marginals, based on the theory of measure transportation, and establishes a vector version of Sklar's theorem. The latter provides a…
Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as…