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Estimation of Distribution Algorithms (EDAs) are implemented mainly by the three steps: selecting the promising subset from the current population, modeling the distribution of the selected population and sampling from the estimated model. Modeling and sampling are key steps of EDAs. They are also research topic of copula theory to represent the multivariate joint distribution by a copula and t...

We study estimation and model selection of semiparametric models of multivariate survival functions for censored data, which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals. We obtain the consistency and root-n asymptotic normality of a two-step copula estimator to the pseudo-true copula parameter value according to KLIC, and provide a simple c...

Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of a...

This paper studies the problem of default correlation. We first introduce a random variable called “timeuntil-default” to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the jo...

This paper studies the problem of default correlation. We first introduce a random variable called “timeuntil-default” to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the jo...

This paper introduces copula functions and the use of the Gaussian copula function to model probabilistic dependencies in supervised classification tasks. A copula is a distribution function with the implicit capacity to model non linear dependencies via concordance measures, such as Kendall’s τ . Hence, this work studies the performance of a simple probabilistic classifier based on the Gaussia...

Consider semiparametric bivariate copula models in which the family of copula functions is parametrized by a Euclidean parameter of interest and in which the two unknown marginal distributions are the (innnite dimensional) nuisance parameters. The eecient score for can be characterized in terms of the solutions of two coupled Sturm-Liouville equations. In case the family of copula functions cor...

Consider semiparametric bivariate copula models in which the family of copula functions is parametrized by a Euclidean parameter θ of interest and in which the two unknown marginal distributions are the (infinite dimensional) nuisance parameters. The efficient score for θ can be characterized in terms of the solutions of two coupled Sturm-Liouville equations. In case the family of copula functi...