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    Enjoy the Joy of Copulas: With a Package copula

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    Copulas have become a popular tool in multivariate modeling successfully applied in many fields. A good open-source implementation of copulas is much needed for more practitioners to enjoy the joy of copulas. This article presents the design, features, and some implementation details of the R package copula. The package provides a carefully designed and easily extensible platform for multivariate modeling with copulas in R. S4 classes for most frequently used elliptical copulas and Archimedean copulas are implemented, with methods for density/distribution evaluation, random number generation, and graphical display. Fitting copula-based models with maximum likelihood method is provided as template examples. With the classes and methods in the package, the package can be easily extended by user-defined copulas and margins to solve problems.

    Goodness-of-fit testing based on a weighted bootstrap: A fast large-sample alternative to the parametric bootstrap

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    The process comparing the empirical cumulative distribution function of the sample with a parametric estimate of the cumulative distribution function is known as the empirical process with estimated parameters and has been extensively employed in the literature for goodness-of-fit testing. The simplest way to carry out such goodness-of-fit tests, especially in a multivariate setting, is to use a parametric bootstrap. Although very easy to implement, the parametric bootstrap can become very computationally expensive as the sample size, the number of parameters, or the dimension of the data increase. An alternative resampling technique based on a fast weighted bootstrap is proposed in this paper, and is studied both theoretically and empirically. The outcome of this work is a generic and computationally efficient multiplier goodness-of-fit procedure that can be used as a large-sample alternative to the parametric bootstrap. In order to approximately determine how large the sample size needs to be for the parametric and weighted bootstraps to have roughly equivalent powers, extensive Monte Carlo experiments are carried out in dimension one, two and three, and for models containing up to nine parameters. The computational gains resulting from the use of the proposed multiplier goodness-of-fit procedure are illustrated on trivariate financial data. A by-product of this work is a fast large-sample goodness-of-fit procedure for the bivariate and trivariate t distribution whose degrees of freedom are fixed.Comment: 26 pages, 5 tables, 1 figur