Consider the model Y = m(X)+ ε, where m(·) = med(Y |·) is unknown but smooth. It is often assumed that ε and X are independent. However, in practice this assumption is in many cases violated. In this paper we propose to model the dependence between ε and X by means of a copula model, i.e. (ε,X) ∼ Cθ(Fε(·), FX(·)), where Cθ is a copula function depending on an unknown parameter θ, and Fε and FX ...

In this paper we propose a method to estimate the value-at-risk (VaR) of a portfolio based on a combination of time series, extreme value theory and copula fitting. Given multivariate financial data, we use a univariate ARMA-GARCH model for each return series. We then fit a generalized Pareto distribution to the tails of the residuals to model the distributions of marginal residuals, followed b...

The multivariate distribution of five main indices of Tehran stock exchange is approximated using a pair-copula model. A vine graphical model is used to produce an í µí±›-dimensional copula. This is accomplished using a flexible copula called a minimum information (MI) copula as a part of pair-copula construction. Obtained results show that the achieved model has a good level of approximation.

We reconsider the existing kernel estimators for a copula function, as proposed in Gijbels and Mielniczuk [Comm. Statist. Theory Methods 19 (1990) 445–464], Fermanian, Radulovič and Wegkamp [Bernoulli 10 (2004) 847–860] and Chen and Huang [Canad. J. Statist. 35 (2007) 265–282]. All of these estimators have as a drawback that they can suffer from a corner bias problem. A way to deal with this is...

In this paper we discuss the problem on parametric and non parametric estimation of the distributions generated by the Marshall-Olkin copula. This copula comes from the Marshall-Olkin bivariate exponential distribution used in reliability analysis. Through this copula we can extend the Marshall-Olkin distribution in order to construct several bivariate survival functions. The cumulative distrib...

Aggregation operators transform a finite number of inputs, called arguments, into a single output. They are applied in many theoretical and practical domains and in particular aggregation operators play important role in different approaches to decision making, where values to be aggregated are typically preference or satisfaction degrees. Many operators of different type have been considered i...

In this paper, a novel approach is proposed based on the probability density function (PDF) concept to achieve the capacity of a correlated ergodic multi-input multi-output (MIMO) channel with Nakagami-m fading. In our proposed method, channel parameters are unknown, and they are initially estimated by using the PDF of the received samples in the receiving antennas. The copula theory is employe...

The generation of multivariate probability distributions follows several approaches. Within financial applications the emphasis has mostly been on two methodologies. The first is the elliptical methodology, where the leap from univariate to multivariate has taken place by constructing density functions that are functions of quadratic forms of the marginals. The second is the copula philosophy, ...

The measure for expert dependence proposed by Jouini and Clemen (clemen) is implemented for expert judgement data gathered at the T.U. Delft. Experts show less dependence than might have been supposed, though more sensitive measures might reveal more. Clemen’s copula for aggregation is implemented and performance is compared with performance-based combinations for two illustrative cases.

Understanding and measuring uncertainty is central in risk analysis. Uncertainty emerges when there is less information than the total information required to describe a system and environment. Uncertainty and information are so closely associated that information provided by an experiment for instance is equal to the amount of uncertainty removed. Uncertainty prevails in several forms and vari...