The aim of this paper is the derivation of the maximum likelihood estimators of the Marshal-Olkin copula. This copula comes from the Marshall-Olkin Bivariate Exponential (MOBE) distribution, that has been proposed in reliability analysis to study complex systems in which the components are not independent and it is also used in the extreme value theory. We find the likelihood estimators conside...

Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, it is common to assume that each of these conditional bivariate copulas is ind...

This research estimates portfolio VaR (Value-at-Risk) on G7 exchange rates using a GJR-GARCH-EVT (extreme value theory)-Copula based approach. We first extracts the filtered residuals from each return series via an asymmetric GJR-GARCH model, then constructs the semi-parametric empirical marginal cumulative distribution function (CDF) of each asset using a Gaussian kernel estimate for the inter...

We study the adaptive estimation of copula correlation matrix for the semi-parametric elliptical copula model. In this context, the correlations are connected to Kendall’s tau through a sine function transformation. Hence, a natural estimate for is the plug-in estimator ̂ with Kendall’s tau statistic. We first obtain a sharp bound on the operator norm of ̂ − . Then we study a factor model of , ...

Given a dependent censored data (X, δ) = (min(T, C), I(T < C)) from an Archimedean copula model, we give general formulas for possible marginal survival functions of T and C. Based on our formulas, we can easily establish the relationship between all these survival functions and derive some useful identifiability results. Also based on our formulas, we propose a new estimator of the marginal su...

A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on a maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity and symmetry constraints for copula density are enforced by linear equality constraints. The TV-M...

In this work, we propose a new framework for learning mixture models from continuous data. Gaussian Mixture Models (GMMs) are commonly used for this task and are popular among practitioners because of their sound statistical foundation and the availability of an efficient learning algorithm [2]. However, the underlying assumption about the normally distributed mixing components, is often too ri...

The extremal dependence of a random vector describes the tail behaviors of joint probabilities of the random vector with respect to that of its margins, and has been often studied by using the tail dependence function of its copula. A tail density approach is introduced in this paper to analyze extremal dependence of the copulas that are specified only by densities. The relation between the cop...

We discuss the general optimization problem of choosing a copula with minimum entropy relative to a specified copula and a computationally intensive procedure to solve its dual. These techniques are applied to constructing an empirical copula for CDO tranche pricing. The empirical copula is chosen to be as close as possible to the industry standard Gaussian copula while ensuring a close fit to ...

In this paper, we address risk aggregation and capital allocation problems in the presence of dependence between risks. The structure is defined by a mixed Bernstein copula which represents generalization well-known Archimedean copulas. Using new copula, probability density function cumulative distribution aggregate are obtained. Then, closed-form expressions for basic measures, such as tail va...