@article { ISI:000366777800013,
	title = {Comparison of non-nested models under a general measure of distance},
	journal = {Journal of Statistical Planning and Inference},
	volume = {170},
	year = {2016},
	month = {MAR},
	pages = {166-185},
	publisher = {Elsevier Science BV},
	type = {Article},
	abstract = {As a supplement to summary statistics of information criteria, the closeness of two or more competing non-nested models can be compared under a procedure that is more general than that proposed in Vuong (1989); measures of closeness other than the Kullback-Leibler divergence are allowed. Large deviation theory is used to obtain a bound of the power of rejecting the null hypothesis that the two models are equally close to the true model. Such a bound can be expressed in terms of a constant gamma is an element of [0, 1); gamma can be computed empirically without any knowledge of the data generating mechanism. Additionally, based on the constant gamma, the procedures constructed based on different measures of distance can be compared on their abilities to conclude a difference between two models. (C) 2015 Elsevier B.V. All rights reserved.},
	keywords = {Composite likelihood, Copula, Large deviation theory, Model comparison, Model misspecification},
	issn = {0378-3758},
	doi = {10.1016/j.jspi.2015.10.004},
	author = {Ng, C. T. 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}
}
@article { ISI:000327908200010,
	title = {Strength of tail dependence based on conditional tail expectation},
	journal = {Journal of Multivariate Analysis},
	volume = {123},
	year = {2014},
	month = {JAN},
	pages = {143-159},
	publisher = {Elsevier Inc},
	type = {Article},
	abstract = {We use the conditional distribution and conditional expectation of one random variable given the other one being large to capture the strength of dependence in the tails of a bivariate random vector. We study the tail behavior of the boundary conditional cumulative distribution function (cdf) and two forms of conditional tail expectation (CTE) for various bivariate copula families. In general, for nonnegative dependence, there are three levels of strength of dependence in the tails according to the tail behavior of CTEs: asymptotically linear, sub-linear and constant. For each of these three levels, we investigate the tail behavior of CTEs for the marginal distributions belonging to maximum domain of attraction of Frechet and Gumbel, respectively, and for copula families with different tail behavior. (C) 2013 Elsevier Inc. All rights reserved.},
	keywords = {Boundary conditional distribution, Copula, intermediate tail dependence, Maximum domain of attraction, Stochastic increasing, Tail behavior, Tail order, Tail quadrant independence},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2013.09.001},
	author = {Hua, Lei and Joe, Harry}
}
@article { ISI:000313478200008,
	title = {Tail comonotonicity and conservative risk measures},
	journal = {ASTIN Bulletin},
	volume = {42},
	number = {2},
	year = {2012},
	month = {NOV},
	pages = {601-629},
	publisher = {Peeters},
	type = {Article},
	abstract = {Tail comonotonicity, or asymptotic full dependence, is proposed as a reasonable conservative dependence structure for modeling dependent risks. Some sufficient conditions have been obtained to justify the conservativity of tail comonotonicity. Simulation studies also suggest that, by using tail comonotonicity, one does not lose too much accuracy but gain reasonable conservative risk measures, especially when considering high scenario risks. A copula model with tail comonotonicity is applied to an auto insurance dataset. Particular models for tail comonotonicity for loss data can be based on the BB2 and BB3 copula families and their multivariate extensions.},
	keywords = {Archimedean copula, asymptotic full dependence, conditional tail expectation, Copula, Dependence modeling, Laplace transform, regular variation},
	issn = {0515-0361},
	doi = {10.2143/AST42.2.2182810},
	author = {Hua, Lei and Joe, Harry}
}
@article { ISI:000309028900029,
	title = {Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures},
	journal = {Insurance Mathematics \& Economics},
	volume = {51},
	number = {2},
	year = {2012},
	month = {SEP},
	pages = {492-503},
	publisher = {Elsevier Science BV},
	type = {Article},
	abstract = {We investigate properties of a version of tail comonotonicity that can be applied to absolutely continuous distributions, and give several methods for constructions of multivariate distributions with tail comonotonicity or strongest tail dependence. Archimedean copulas as mixtures of powers, and scale mixtures of a non-negative random vector with the mixing distribution having slowly varying tails, lead to a tail comonotonic dependence structure. For random variables that are in the maximum domain of attraction of either Frechet or Gumbel, we prove the asymptotic additivity property of Value at Risk and Conditional Tail Expectation. (C) 2012 Elsevier B.V. All rights reserved.},
	keywords = {Archimedean copula, asymptotic full dependence, Copula, Elliptical distributions, Extreme value distributions, Regularly varying, Slowly varying},
	issn = {0167-6687},
	doi = {10.1016/j.insmatheco.2012.07.006},
	author = {Hua, Lei and Joe, Harry}
}
@article { ISI:000299151700002,
	title = {Tail risk of multivariate regular variation},
	journal = {Methodology and Computing in Applied Probability},
	volume = {13},
	number = {4},
	year = {2011},
	month = {DEC},
	pages = {671-693},
	publisher = {Springer},
	type = {Article},
	abstract = {Tail risk refers to the risk associated with extreme values and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expectation, is analyzed for multivariate regularly varying distributions. Asymptotic expressions for tail risk are established in terms of the intensity measure that characterizes multivariate regular variation. Tractable bounds for tail risk are derived in terms of the tail dependence function that describes extremal dependence. Various examples involving Archimedean copulas are presented to illustrate the results and quality of the bounds.},
	keywords = {Coherent risk, Copula, Regularly varying, Tail conditional expectation, Tail dependence},
	issn = {1387-5841},
	doi = {10.1007/s11009-010-9183-x},
	author = {Joe, Harry and Li, Haijun}
}
@conference { ISI:000238122900008,
	title = {Range of correlation matrices for dependent random variables with given marginal distributions},
	booktitle = {Advances in Distribution Theory, Order Statistics, and Inference},
	series = {Statistics for Industry and Technology},
	year = {2006},
	note = {International Conference on Distribution Theory, Order Statistics, and Inference, Univ Cantabria, Santander, SPAIN, JUN 16-18, 2004},
	pages = {125-142},
	publisher = {Birkhauser Boston},
	organization = {Birkhauser Boston},
	type = {Proceedings Paper},
	abstract = {Let X-1, center dot center dot center dot, X-d be d (d >= 3) dependent random variables with finite variances such that X-j similar to F-j. Results on the set S-d(F-1, center dot center dot center dot, F-d) of possible correlation matrices with given margins are obtained; this set is relevant for simulating dependent random variables with given marginal distributions and a given correlation matrix. When F-1 = (...) = F-d = F, we let S-d(F) denote the set of possible correlation matrices. Of interest is the set of F for which Sd(F) is the same as the set of all non-negative definite correlation matrices; using a construction with conditional distributions, we show that this property holds only if F is a (location-scale shift of a) margin of a (d-1)-dimensional spherical distribution.},
	keywords = {Copula, elliptically contoured, Frechet bounds, Partial correlation, spherically symmetric},
	isbn = {0-8176-4361-3},
	doi = {10.1007/0-8176-4487-3_8},
	author = {Joe, Harry},
	editor = {Balakrishnan, N and Castillo, E and Sarabia, J. M.}
}
