In this review paper we outline some recent contributions to copula theory. Several new author's investigations are presented brie°y, namely: order statistics copula, copulas with given multivariate marginals, copula representation via a local dependence measure and applications of extreme value copulas. Key-words: Copula; Dependence measures; Extremes; Kendall distribution; Local dependence; M...

Existing works on multivariate distributions mainly focus on limited distribution functions and require that the associated marginal distributions belong to the same family. Although this simplifies problems, it may fail to deal with practical cases when the marginal distributions are arbitrary. To this end, copula function is employed since it provides a flexible way in decoupling the marginal...

We apply a copula-GARCH approach to modeling the joint distribution of excess returns of four major assets: one year and ten year Treasury bonds and S&P 500 and Nasdaq indices. We try three approaches in building the multidimensional copula for the dependence structure of multiple variables: (1) n-dimensional normal copula and n-dimensional Student’s t copula, (2) hierarchical Archimedean copul...

Copula is an important tool for modeling neural dependence. Recent work on copula has been expanded to jointly model mixed time series in neuroscience ("Hu et al., 2016, Joint Analysis of Spikes and Local Field Potentials using Copula" [1]). Here we present further data for joint analysis of spike and local field potential (LFP) with copula modeling. In particular, the details of different mode...

The copula-based modeling of multivariate distributions with continuous margins is presented as a succession of rank-based tests: a multivariate test of randomness followed by a test of mutual independence and a series of goodness-of-fit tests. All the tests under consideration are based on the empirical copula, which is a nonparametric rank-based estimator of the true unknown copula. The princ...

We tackle the challenge of efficiently learning the structure of expressive multivariate realvalued densities of copula graphical models. We start by theoretically substantiating the conjecture that for many copula families the magnitude of Spearman’s rank correlation coefficient is monotonic in the expected contribution of an edge in network, namely the negative copula entropy. We then build o...

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...