@article { ISI:000355774000005,
	title = {Structured factor copula models: Theory, inference and computation},
	journal = {Journal of Multivariate Analysis},
	volume = {138},
	number = {SI},
	year = {2015},
	month = {JUN},
	pages = {53-73},
	publisher = {Elsevier Inc},
	type = {Article},
	abstract = {In factor copula models for multivariate data, dependence is explained via one or several common factors. These models are flexible in handling tail dependence and asymmetry with parsimonious dependence structures. We propose two structured factor copula models for the case where variables can be split into non-overlapping groups such that there is homogeneous dependence within each group. A typical example of such variables occurs for stock returns from different sectors. The structured models inherit most of dependence properties derived for common factor copula models. With appropriate numerical methods, efficient estimation of dependence parameters is possible for data sets with over 100 variables. We apply the structured factor copula models to analyze a financial data set, and compare with other copula models for tail inference. Using model-based interval estimates, we find that some commonly used risk measures may not be well discriminated by copula models, but tail-weighted dependence measures can discriminate copula models with different dependence and tail properties. (C) 2014 Elsevier Inc. All rights reserved.},
	keywords = {Bi-factor model, Conditional independence, Dependence measure, Factor analysis, Tail asymmetry, Tail dependence, Truncated vine},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2014.11.002},
	author = {Krupskii, Pavel and Joe, Harry}
}
@article { ISI:000346333600012,
	title = {Tail-weighted measures of dependence},
	journal = {Journal of Applied Statistics},
	volume = {42},
	number = {3},
	year = {2015},
	month = {MAR 4},
	pages = {614-629},
	publisher = {Taylor \& Francis Ltd},
	type = {Article},
	abstract = {Multivariate copula models are commonly used in place of Gaussian dependence models when plots of the data suggest tail dependence and tail asymmetry. In these cases, it is useful to have simple statistics to summarize the strength of dependence in different joint tails. Measures of monotone association such as Kendall{\textquoteright}s tau and Spearman{\textquoteright}s rho are insufficient to distinguish commonly used parametric bivariate families with different tail properties. We propose lower and upper tail-weighted bivariate measures of dependence as additional scalar measures to distinguish bivariate copulas with roughly the same overall monotone dependence. These measures allow the efficient estimation of strength of dependence in the joint tails and can be used as a guide for selection of bivariate linking copulas in vine and factor models as well as for assessing the adequacy of fit of multivariate copula models. We apply the tail-weighted measures of dependence to a financial data set and show that the measures better discriminate models with different tail properties compared to commonly used risk measures - the portfolio value-at-risk and conditional tail expectation.},
	keywords = {62H20, Copula, Dependence measure, factor model, intermediate tail dependence, Tail asymmetry, Tail dependence},
	issn = {0266-4763},
	doi = {10.1080/02664763.2014.980787},
	author = {Krupskii, Pavel and Joe, Harry}
}
