Article2012

Pair Copula Constructions for Multivariate Discrete Data

Anastasios Panagiotelis · Claudia Czado · Harry Joe

194 citations0/0 files storedJournal of the American Statistical Association

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Financial Risk and Volatility Modeling Statistical Distribution Estimation and Applications Bayesian Modeling and Causal Inference

Abstract

Multivariate discrete response data can be found in diverse fields, including econometrics, finance, biometrics, and psychometrics. Our contribution, through this study, is to introduce a new class of models for multivariate discrete data based on pair copula constructions (PCCs) that has two major advantages. First, by deriving the conditions under which any multivariate discrete distribution can be decomposed as a PCC, we show that discrete PCCs attain highly flexible dependence structures. Second, the computational burden of evaluating the likelihood for an m-dimensional discrete PCC only grows quadratically with m. This compares favorably to existing models for which computing the likelihood either requires the evaluation of 2 m terms or slow numerical integration methods. We demonstrate the high quality of inference function for margins and maximum likelihood estimates, both under a simulated setting and for an application to a longitudinal discrete dataset on headache severity. This article has online supplementary material.

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References

2007Pair-copula constructions of multiple dependence 1996Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters 2006Uncertainty Analysis with High Dimensional Dependence Modelling 2010Dependence Modeling: Vine Copula Handbook 2007A Primer on Copulas for Count Data 2009Tail dependence functions and vine copulas 2012Truncated regular vines in high dimensions with application to financial data 2010Pair-Copula Constructions of Multivariate Copulas

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