Copulas are full measures of dependence among components of random vectors. Unlike the marginal and the joint distributions, which are directly observable, a copula is a hidden dependence structure that couples a joint distribution with its marginals. This makes the task of proposing a parametric copula model non-trivial and is where a nonparametric estimator can play a significant role. In thi...

One main complexity of the copula constructions concerns a mismatch between morphology and syntactic constituency: the copula seems to form a morphological unit with the immediately preceding element, whereas in terms of syntax the copula appears to take this as its syntactic complement. In capturing such mismatches, we show that the copula is treated as an independent verb at the level of tect...

This paper presents the role of copula functions in the theory of aggregation operators and an axiomatic characterization of Archimedean aggregation functions. In this context we are focusing our attention about several properties of aggregation functions, like supermodularity and Schur-concavity.

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 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...