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Modelling dependance between the two uncorrelated variables using copulas

Uncorrelated does not imply independent, hence a copula could capture the dependence for very small correlations if there is any. As an example, the student t copula with a degree of freedom of 0.4 ...
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Book suggestions for model validation (Gini, Somers D, Kolmogorov Smirnov, Kendal's Tau, Binomial/Adjusted binomial test etc)

Risk Model Validation: A practical guide to addressing the key questions by Christian Meyer and Peter Quell. The Validation of Risk Models: A Handbook for Practitioners by Sergio Scandizzo.
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1 vote

Book suggestions for model validation (Gini, Somers D, Kolmogorov Smirnov, Kendal's Tau, Binomial/Adjusted binomial test etc)

The Basel working paper contains quite a comprehensive summary of the types of metrics you are looking for: https://www.bis.org/publ/bcbs_wp14.pdf
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