As multivariate distributions with uniform one-dimensional margins, copulas provide very convenient models for studying dependence structure with tools that are scale-free. Each copula (n-copula) represents the whole class of continuous bivariate (multivariate) distributions from which it has been obtained when one-dimensional marginals were transformed by their cdf’s. The similar property, how...

In this paper we provide three nonparametric tests of independence between continuous random variables based on Bernstein copula and copula density. The first test is constructed based on functional of Cramér-von Mises of the Bernstein empirical copula. The two other tests are based on Bernstein density copula and use Cramér-von Mises and Kullback-Leiber divergencetype respectively. Furthermore...

The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. To overcome the calibration deficiency, we introduce a multi-period factor copula model by chaining one-period factor copula models. The correlation coefficients in our model are...

A Skewed Student-t Realised DCC copula model using Realised Volatility GARCH marginal functions is developed within a Bayesian framework for the purpose of forecasting portfolio Value at Risk and Conditional Value at Risk. The use of copulas is implemented so that the marginal distributions can be separated from the dependence structure to produce tail forecasts. This is compared to using tradi...

In this paper we obtain robust estimators for copula parameters through the minimization of weighted goodness of ̄t statistics. Di®erent weight functions emphasize di®erent regions on the unit square and are able to handle di®erent locations of model violation. The resultingWMDE estimators are compared to the classical maximum likelihood estimatorsMLE, and to their weighted version WMLE, an est...

Contemporary computers collect databases that can be too large for classical methods to handle. The present work takes data whose observations are distribution functions (rather than the single numerical point value of classical data) and presents the computational statistical approach of a new methodology to group the distributions into classes. The clustering method links the searched partiti...

Graphical models are widely used to reason about high-dimensional domains. Yet, learning the structure of the model from data remains a formidable challenge, particularly in complex continuous domains. We present a highly accelerated structure learning approach for continuous densities based on the recently introduced Copula Bayesian Network representation. For two common copula families, we pr...

This paper develops a joint copula reliability model for systems subjected to dependent competing risks caused by two degradation processes and random shocks. The two degradation processes follow gamma processes and the random shocks follow a non-homogeneous Poisson process (NHPP). Their interdependence relationship is modeled by a copula function, which is determined by a two-stage method base...

Parametric conditional copulamodels allow the copula parameters to vary with a set of covariates according to an unknown calibration function. Flexible Bayesian inference for the calibration function of a bivariate conditional copula is introduced. The prior distribution over the set of smooth calibration functions is built using a sparse Gaussian process (GP) prior for the single index model (...