Algorithmic inference approach to learn copulas

We introduce a new method for estimating the parameter α of the Clayton copulas within the framework of Algorithmic Inference. The method consists of a variant of the standard bootstrapping 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, customary 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 α estimate at a fixed point of an iterative routine. Numerical results show a good accuracy of the estimates, though paired in some cases with the complexity of the programs which compute them.