VineCopulas.jl

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References ​

This page lists the main references behind the mathematical and computational design of VineCopulas.jl. The package documentation cites concepts in prose rather than using a bibliography engine, to keep the documentation build small and stable.

Copulas and Sklar composition ​

  • Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut de Statistique de l'Université de Paris.

  • Nelsen, R. B. (2006). An Introduction to Copulas. Springer.

  • Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall.

  • McNeil, A. J., Frey, R., and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press.

Pair-copula constructions and vines ​

  • Bedford, T., and Cooke, R. M. (2001). Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence.

  • Bedford, T., and Cooke, R. M. (2002). Vines: A new graphical model for dependent random variables. The Annals of Statistics.

  • Aas, K., Czado, C., Frigessi, A., and Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics.

  • Joe, H. (2014). Dependence Modeling with Copulas. Chapman & Hall/CRC.

  • Kurowicka, D., and Joe, H. (2011). Dependence Modeling: Vine Copula Handbook. World Scientific.

Structure selection and truncation ​

  • Dißmann, J., Brechmann, E. C., Czado, C., and Kurowicka, D. (2013). Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis.

  • Brechmann, E. C., Czado, C., and Aas, K. (2012). Truncated regular vines in high dimensions with application to financial data. Canadian Journal of Statistics.

  • Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society.

  • Brechmann, E. C., and Czado, C. (2013). Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50. Statistics & Risk Modeling. (The regular-vine market-sector model.)

  • Müller, D., and Czado, C. (2019). Dependence modelling in ultra high dimensions with vine copulas and the graphical Lasso. Computational Statistics & Data Analysis. (Candidate-edge restriction.)

  • Guttmann-Beck, N., Sorek, Z., and Stern, M. (2019). Clustered spanning tree — conditions for feasibility. Discrete Mathematics & Theoretical Computer Science, 21(1).

  • D'Emidio, M., Forlizzi, L., Frigioni, D., Leucci, S., and Proietti, G. (2019). Hardness, approximability, and fixed-parameter tractability of the clustered shortest-path tree problem. Journal of Combinatorial Optimization, 38(1), 165–184.

Dependence measures used as tree criteria ​

  • Kendall, M. G. (1938). A new measure of rank correlation. Biometrika.

  • Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology.

  • Hoeffding, W. (1948). A non-parametric test of independence. The Annals of Mathematical Statistics.

  • Hollander, M., Wolfe, D. A., and Chicken, E. (2014). Nonparametric Statistical Methods, 3rd ed. Wiley. (The computational form of Hoeffding's .)

  • Gebelein, H. (1941). Das statistische Problem der Korrelation als Variations- und Eigenwertproblem und sein Zusammenhang mit der Ausgleichsrechnung. Zeitschrift für Angewandte Mathematik und Mechanik.

  • Rényi, A. (1959). On measures of dependence. Acta Mathematica Academiae Scientiarum Hungaricae.

  • Breiman, L., and Friedman, J. H. (1985). Estimating optimal transformations for multiple regression and correlation. Journal of the American Statistical Association. (The ACE algorithm behind tree_criterion=:mcor.)

  • Joe, H. (1989). Relative entropy measures of multivariate dependence. Journal of the American Statistical Association. (tree_criterion=:joe.)

  • Chatterjee, S. (2021). A new coefficient of correlation. Journal of the American Statistical Association. (tree_criterion=:cxi.)

Rosenblatt transforms and diagnostics ​

  • Rosenblatt, M. (1952). Remarks on a multivariate transformation. The Annals of Mathematical Statistics.

  • Genest, C., Rémillard, B., and Beaudoin, D. (2009). Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics.

Software ecosystem ​

  • Laverny, O., and Jimenez, S. (2024). Copulas.jl: A fully Distributions.jl-compliant copula package. Journal of Open Source Software.

  • Nagler, T., Vatter, T., and colleagues. vinecopulib and rvinecopulib documentation and software releases.

  • Besançon, M., Papamarkou, T., Anthoff, D., et al. (2021). Distributions.jl: Definition and modeling of probability distributions in the JuliaStats ecosystem. Journal of Statistical Software.

For contributors

Add references when a page introduces a mathematical definition, a selection algorithm, or a benchmark reference implementation. API pages usually do not need literature citations unless an exported function implements a named statistical criterion.