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We present a new way of constructing n-copulas, by scaling and gluing finitely many n-copulas. Gluing for bivariate copulas produces a copula that coincides with the independence copula on some grid of horizontal and vertical sections. Examples illustrate how gluing can be applied to build complicated copulas from simple ones. Finally, we investigate the analytical as well as statistical properties of the copulas obtained by gluing, in particular, the behavior of Spearman's ρ and Kendall's τ. [ABSTRACT FROM AUTHOR]

We generalize the extreme value analysis for Archimedean copulas (seeAlink,Löwe andWüthrich, 2003) to the non-Archimedean case: Assume we have d≥2 exchangeable and continuously distributed risks X1,..., X d. Under appropriate assumptions there is a constant q d such that, for all large u, we have . The constant q d describes the asymptotic dependence structure. Typically, q d will depend on more aspects of this dependence structure than the well-known tail dependence coefficient. [ABSTRACT FROM AUTHOR]

We present a method which reduces the Kolmogorov goodness-of-test of independence to the Kolmogorov-Smimov one sample test. The null distribution of test statistic is the same as the Kolmogorov-Smimov test statistic in this test of independence. [ABSTRACT FROM AUTHOR]

The article presents the author's comments on the paper "Model Selection and Semiparametric Interference for Bivariate Failure-Time Data," by Weijing Wang and Martin T. Wells. Wang and Wells have presented an interesting method for selecting the Archimedean copula (AC) model for bivariate failure time data in the presence of right cursoring. The intent of these comments is to call attention to the issue of whether one should standardize statistics in model selection procedures when nuisance parameters are estimated. The model selection procedure proposed by Wang and Wells is but one example in which this issue arises. This situation occurs in other statistical models, such as in parametric model discrimination with right-censored data where the nuisance parameters are the parametric model parameters and the discrimination statistics are based on generalized residuals. The question of whether or not to standardize the statistics before using them for selecting the model, which is an analogous problem to that encountered by Wang and Wells, arises. It is thus of prime interest to further study this aspect more rigorously and substantively so that a definitive resolution on whether or not to standardize can be made.

The article focuses on copulas. The author provided brief information on the introduction of copulas and its application in various areas like finance, risk-management and hydrology. Moreover, he mentioned several papers, books, conferences and symposiums that discussed copulas like "Probabilistic Metric Spaces," by A. Sklar, and others.