×

Pair copula constructions for multivariate discrete data. (English) Zbl 1395.62114

Summary: 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.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H12 Estimation in multivariate analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Aas K., Insurance, Mathematics and Economics 44 pp 182– (2009) · Zbl 1165.60009
[2] Bedford T., The Annals of Mathematics and Artificial Intelligence 32 pp 245– (2001) · Zbl 1314.62040
[3] Bedford T., The Annals of Statistics 30 pp 1031– (2002) · Zbl 1101.62339
[4] Brechmann E., Canadian Journal of Statistics 40 pp 68– (2012) · Zbl 1274.62381
[5] Clarke K., Political Analysis 13 pp 347– (2007)
[6] Czado C., Workshop on Copula Theory and Its Applications pp 93– (2010)
[7] Denuit M., Journal of Multivariate Analysis 93 pp 40– (2005) · Zbl 1095.62065
[8] Genest C., The Astin Bulletin 37 pp 475– (2007) · Zbl 1274.62398
[9] Hu F., Canadian Journal of Statistics 28 pp 449– (2000) · Zbl 0977.62045
[10] Joe H., Distributions With Fixed Marginals and Related Topics pp 20– (1996)
[11] Joe H., Multivariate Models and Dependence Concepts, Monographs on Statistics and Applied Probability (1997) · Zbl 0990.62517
[12] Joe H., Journal of Multivariate Analysis 101 pp 252– (2010) · Zbl 1177.62072
[13] Kurowicka D., Uncertainty Analysis With High Dimensional Dependence Modelling(Wiley Series in Probability and Statistics) (2006) · Zbl 1096.62073
[14] Kurowicka D., Dependence Modeling: Vine Copula Handbook (2011)
[15] Li J., Biostatistics 12 pp 143– (2011)
[16] Nelsen R., An Introduction to Copulas(Springer Series in Statistics) (2nd ed.) (2006) · Zbl 1152.62030
[17] Nikoloulopoulos A., Statistics in Medicine 27 pp 6393– (2008)
[18] Nikoloulopoulos A., Journal of Statistical Planning and Inference 139 pp 3878– (2009) · Zbl 1169.62044
[19] Sklar A., Publications of the Institute of Statistics, University of Paris 8 pp 229– (1959)
[20] Smith M., Journal of the American Statistical Association 107 pp 290– (2012) · Zbl 1261.62051
[21] Smith M., Journal of the American Statistical Association 105 pp 1467– (2010) · Zbl 1388.62171
[22] Song P. X-K, Biometrics 65 pp 60– (2009) · Zbl 1159.62049
[23] Varin C., Biostatistics 11 pp 127– (2010)
[24] Vuong Q., Econometrica 57 pp 307– (1989) · Zbl 0701.62106
[25] Zhao Y., Canadian Journal of Statistics 33 pp 335– (2005) · Zbl 1077.62045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.