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Motivated by recently investigated results on dependence measures and robust risk models, this paper provides an overview of dependence properties of many well-known bivariate copula families, where the focus is on the Schur order for…
Copula models of multivariate data are popular because they allow separate specification of marginal distributions and the copula function. These components can be treated as inter-related modules in a modified Bayesian inference approach…
Building higher-dimensional copulas is generally recognized as a difficult problem. Regular-vines using bivariate copulas provide a flexible class of high-dimensional dependency models. In large dimensions, the drawback of the model is the…
This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
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…
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,…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
This paper introduces a new class of Cox models for dependent bivariate data. The impact of the covariate on the dependence of the variables is captured through the modification of their copula. Various classes of well known copulas are…
Sarmanov copulas offer a simple and tractable way to build multivariate distributions by perturbing the independence copula. They admit closed-form expressions for densities and many functionals of interest, making them attractive for…
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…
A notion of tail dependence based on operator regular variation is introduced for copulas, and the standard tail dependence used in the copula literature is included as a special case. The non-standard tail dependence with marginal power…
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences…
A factor copula model is proposed in which factors are either simulable or estimable from exogenous information. Point estimation and inference are based on a simulated methods of moments (SMM) approach with non-overlapping simulation…
We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter…
Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model,…
Maximum pseudo-likelihood (MPL) is a semiparametric estimation method often used to obtain the dependence parameters in copula models from data. It has been shown that despite being consistent, and in some cases efficient, MPL estimation…
Cylindrical data frequently arise across various scientific disciplines, including meteorology (e.g., wind direction and speed), oceanography (e.g., marine current direction and speed or wave heights), ecology (e.g., telemetry), and…
Statistical inference in high-dimensional settings is challenging when standard unregularized methods are employed. In this work, we focus on the case of multiple correlated proportions for which we develop a Bayesian inference framework.…
This paper deals with robust inference for parametric copula models. Estimation using Canonical Maximum Likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the Maximum Mean…