An Algorithmic Inference Approach to Learn Copulas
This work addresses a specific statistical inference problem for copula modeling, but it is incremental as it builds on existing bootstrapping methods with targeted improvements.
The authors tackled the problem of estimating parameters for bivariate Clayton copulas by introducing a variant of bootstrapping within Algorithmic Inference to address issues like non-independence of Kendall statistics and lack of sufficient statistics. The result was an outperforming accuracy in estimates, as shown by numerical results.
We introduce a new method for estimating the parameter of the bivariate Clayton copulas within the framework of Algorithmic Inference. The method consists of a variant of the standard boot-strapping procedure for inferring random parameters, which we expressly devise to bypass the two pitfalls of this specific instance: the non independence of the Kendall statistics, customarily at the basis of this inference task, and the absence of a sufficient statistic w.r.t. α. The variant is rooted on a numerical procedure in order to find the αestimate at a fixed point of an iterative routine. Although paired with the customary complexity of the program which computes them, numerical results show an outperforming accuracy of the estimates.