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• W2617018756 abstract "AbstractA popular approach for modeling dependence in a finite-dimensional random vectorX with given univariate marginals is via a normal copula that fits the rank or linearcorrelations for the bivariate marginals of X. In this approach, known as the NORTAmethod, the normal distribution function is applied to each coordinate of a vector Zof correlated standard normals to produce a vector U of correlated uniforms randomvariables over (0,1); then X is obtained by applying the inverse of the target marginaldistribution function for each coordinate of U. The fitting requires finding the ap-propriate correlation ρ between any two given coordinates of Z that would yield thetarget rank or linear correlation r between the corresponding coordinates of X. Thisroot-finding problem is easy to solve when the marginals are continuous, but not whenthey are discrete. In this paper, we provide a detailed analysis of the NORTA methodfor discrete marginals. We prove key properties of r and of its derivative as a functionof ρ. It turns out that the derivative is easier to evaluate than the function itself.Based on that, we propose and compare alternative methods for finding or approxi-mating the appropriate ρ. The case of discrete distributions with unbounded supportis covered as well. In our numerical experiments, a derivative-supported method isfaster and more accurate than a state-of-the-art, non-derivative-based method. Wealso characterize the asymptotic convergence rate of the function r (as a function of ρ)to the continuous-marginals limiting function, when the discrete marginals convergeto continuous distributions.Key Words: Statistics; distribution; estimation; correlation; mathematics; simula-tion.Acknowledgments: This work has been supported by a grant from Bell Canada viathe Bell University Laboratories, Grants No. CRDPJ-251320 and ODGP0110050 fromNSERC-Canada, and a Canada Research Chair to the third author. We thank RichardSimard for his assistance in programming aspects and some numerical experiments." @default.
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• W2617018756 date "2006-11-01" @default.
• W2617018756 modified "2023-10-15" @default.
• W2617018756 title "Efficient Correlation Matching for Normal-Copula Dependence when Univariate Marginals Are Discrete" @default.
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