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Multivariate models for dependent clusters of variables with conditional independence given aggregation variables

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  • Joe, Harry
  • Sang, Peijun

Abstract

A general multivariate distributional approach, with conditional independence given aggregation variables, is presented to combine group-based submodels when variables are naturally divided into several non-overlapping groups. When the distributions are all multivariate Gaussian, the dependence among different groups is parsimonious based on conditional independence given linear combinations of variables in each group. For the case of multivariate t distributions in each group, a grouped t distribution is obtained. The approach can be extended so that the copula for each group is based on a skew-t distribution, and an application of this is given to financial returns of stocks in several different sectors. Another example of the modeling approach is given with variables separated into groups based on their units of measurements.

Suggested Citation

  • Joe, Harry & Sang, Peijun, 2016. "Multivariate models for dependent clusters of variables with conditional independence given aggregation variables," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 114-132.
    • Handle: RePEc:eee:csdana:v:97:y:2016:i:c:p:114-132
    DOI: 10.1016/j.csda.2015.12.001
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    References listed on IDEAS

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    1. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 73-85.
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    6. Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    7. Krupskii, Pavel & Joe, Harry, 2015. "Structured factor copula models: Theory, inference and computation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 53-73.
    8. Thomas Fung & Eugene Seneta, 2010. "Tail dependence and skew distributions," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 327-333.
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    Cited by:

    1. Hua, Lei & Joe, Harry, 2017. "Multivariate dependence modeling based on comonotonic factors," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 317-333.
    2. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.

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