A neat way of quantifying arbitrary (?) dependence structures between random variables. Useful in, e.g. Quantitative Risk Management.
The trick is simple: Informally, you look at the marginal iCDF of each of \(n\) variables, and fiddle with the joint distribution of those marginals on \([0,1]^n\). (That’s assuming variables are absolutely continuous w.r.t some underlying measure space; distribution with atoms are trickier.)
This is a good trick, although I need to sit down and think through it. I would like to better understand:
- the relationship between the underlying event space and the instrumental one we “sort of” construct in copula modeling.
- Is any information lost with non-monotonic coupling in a copula model?
- conditional copulas and how they work
- the occasionally-mentioned relationship between copula entropy and mutual information.
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Chen, Song Xi, and Tzee-Ming Huang. 2007. “Nonparametric Estimation of Copula Functions for Dependence Modelling.” Canadian Journal of Statistics 35 (2): 265–82. https://doi.org/10.1002/cjs.5550350205.
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