We propose an approach for dependence tree structure learning via copula. A nonparametric algorithm for copula estimation is presented. Then a Chow-Liu like method based on dependence measure via copula is proposed to estimate maximum spanning bivariate copula associated with bivariate dependence relations. The main advantage of the approach is that learning with empirical copula focuses on dep...

It is well known that the empirical copula process converges weakly to a centered Gaussian field. Because the covariance structure of the limiting process depends on the partial derivatives of the unknown copula several bootstrap approximations for the empirical copula process have been proposed in the literature. We present a brief review of these procedures. Because some of these procedures a...

Article history: Received 7 August 2009 Received in revised form 10 September 2009 Accepted 10 September 2009 Available online 19 September 2009 We investigate tail risk in emerging stock markets at the country, regional and world levels, by comparing the investable and noninvestable segments in terms of the expected shortfall of standardized returns and tail dependence on the world market. Emp...

In dose-finding clinical study, it is common that multiple endpoints are of interest. For instance, efficacy and toxicity endpoints are both primary in clinical trials. In this article, we propose a joint model for correlated efficacy-toxicity outcome constructed with Archimedean Copula, and extend the continual reassessment method (CRM) to a bivariate trial design in which the optimal dose for...

Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula theories provides new insights in hydrologic modeling and analysis, for which the...

We show that all multivariate Extreme Value distributions, which are the possible weak limits of the K largest order statistics of iid sequences, have the same copula, the so called K-extremal copula. This copula is described through exact expressions for its density and distribution functions. We also study measures of dependence, we obtain a weak convergence result and we propose a simulation...

Vine copula models have proven themselves as a very flexible class of multivariate copula models with regard to symmetry and tail dependence for pairs of variables. The full specification of a vine model requires the choice of vine tree structure, copula families for each pair copula term and their corresponding parameters. In this survey we discuss the different approaches, both frequentist as...

With the aim of portfolio optimization and management, this article utilizes the Clayton-copula along with copula theory measures. Portfolio-Optimization is one of the activities in investment funds. Thus, it is essential to select an appropriate optimization method. In modern financial analyses, there is growing evidence indicating the distribution of proceeds of financial properties is not cu...

In information theory, mutual information (MI) is a difference concept with entropy.[1] In this paper, we prove with copula [2] that they are essentially same – mutual information is also a kind of entropy, called copula entropy. Based on this insightful result, We propose a simple method for estimating mutual information. Copula is a theory on dependence and measurement of association.[2] Skla...

We consider the problem of accurately measuring the credit risk of a portfolio consisting of loans, bonds and other financial assets. One particular performance measure of interest is the probability of large portfolio losses over a fixed time horizon. We revisit the so-called t-copula that generalizes the popular normal copula to allow for extremal dependence among defaults. By utilizing the a...