Sampling Count Variables with Specified Pearson Correlation: A Comparison Between a Naive and a C-Vine Sampling Approach

Vinzenz Erhardt and Claudia Czado
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Vinzenz Erhardt: Technische Universität München, Zentrum Mathematik, Boltzmannstr. 3, 85747 Garching, Germany
Claudia Czado: Technische Universität München, Zentrum Mathematik, Boltzmannstr. 3, 85747 Garching, Germany

Chapter 4 in Dependence Modeling:Vine Copula Handbook, 2010, pp 73-87 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractErhardt and Czado11 suggest an approximative method for sampling high-dimensional count random variables with a specified Pearson correlation. They utilize Gaussian copulae for the construction of multivariate discrete distributions. A major task is to determine the appropriate copula parameters for the achievement of a specified target correlation. Erhardt and Czado11 develop an optimization routine to determine these copula parameters sequentially. Thereby, they use pair-copula decompositions of n-dimensional distributions, i.e., a decomposition consisting only of bivariate copula with one parameter each. C-vines, a graphical tool to organize such pair-copula decompositions, are used to select a possible decomposition. In the paper mentioned, the approach was compared to the NORTA method for discrete margins described in Ref. 2. Here, we will compare it to a widely used naive sampling approach for an even larger variety of marginal distributions such as the Poisson, generalized Poisson, negative binomial and zero-inflated generalized Poisson distributions.

Keywords: Dependence Modeling; Joint Distributions; Copulae; Vines; Graphical Models; PCC (search for similar items in EconPapers)
Date: 2010
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