Related papers: Modeling directional monotonicity with copulas
In this paper the problems of the retrospective analysis of models with time-varying structure are considered. These models include contamination models with randomly switching parameters and multivariate classification models with an…
We are studying the problems of modeling and inference for multivariate count time series data with Poisson marginals. The focus is on linear and log-linear models. For studying the properties of such processes we develop a novel conceptual…
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…
Following our previous work on copula-based nonsymmetric bivariate dependence measures, we propose a new set of conditions on nonsymmetric multivariate dependence measures which characterize both independence and complete dependence of one…
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…
In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. We introduce the concept of multivariate discrete copulas, discuss their equivalence to…
In this note, we study monotone dynamical systems with respect to polyhedral cones. Using the half-space representation and the vertex representation, we propose three equivalent conditions to certify monotonicity of a dynamical system with…
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…
Cyclic monotone independence is an algebraic notion of noncommutative independence, introduced in the study of multi-matrix random matrix models with small rank. Its algebraic form turns out to be surprisingly close to monotone…
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…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
We introduce a new family of copula densities constructed from univariate distributions on $[0,1]$. Although our construction is structurally simple, the resulting family is versatile: it includes both smooth and irregular examples, and…
We point out the connection of the so-called H\^opital-style rules for monotonicity and oscillation to some well-known properties of concave/convex functions. From this standpoint, we are able to generalize the rules under no…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
This is an outline of work in progress. We study the conjecture that the topological entropy of a real cubic map depends ``monotonely'' on its parameters, in the sense that each locus of constant entropy in parameter space is a connected…
This paper introduces a new class of observation driven dynamic models. The time evolving parameters are driven by innovations of copula form. The resulting models can be made strictly stationary and the innovation term is typically chosen…
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
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…
The main goal of this paper is to show how some monotonicity methods related with the subdifferential of suitable convex functions and its extensions as m-accretive operators in Banach spaces lead to new and unexpected results showing, for…
The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…