@article { ISI:000309793400023,
	title = {Pair copula constructions for multivariate discrete data},
	journal = {Journal of the American Statistical Association},
	volume = {107},
	number = {499},
	year = {2012},
	month = {SEP},
	pages = {1063-1072},
	publisher = {Amer Statistical Assoc},
	type = {Article},
	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 in. 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.},
	keywords = {D-vine, Inference function for margins, Longitudinal data, Model selection, Ordered probit regression},
	issn = {0162-1459},
	doi = {10.1080/01621459.2012.682850},
	author = {Panagiotelis, Anastasios and Czado, Claudia and Joe, Harry}
}
@article { ISI:000272526200019,
	title = {Tail dependence functions and vine copulas},
	journal = {Journal of Multivariate Analysis},
	volume = {101},
	number = {1},
	year = {2010},
	month = {JAN},
	pages = {252-270},
	publisher = {Elsevier Inc},
	type = {Article},
	abstract = {Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities Of a Copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a, copula, as described by its extreme Value copulas, is shown to be completely determined by its tail dependence functions. For a vine Copula built from a set of bivariate copulas, its tail dependence function can be expressed recursively by the tail dependence and conditional tail dependence functions of lower-dimensional margins. The effect of tail dependence of bivariate linking copulas on that of a vine copula is also investigated. (C) 2009 Elsevier Inc. All rights reserved.},
	keywords = {Archimedean copulas, C-vine, Conditional tail, D-vine, Extreme value},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2009.08.002},
	author = {Joe, Harry and Li, Haijun and Nikoloulopoulos, Aristidis K.}
}
