An Algorithmic Inference Approach to Learn Copulas

TL;DR

This paper presents a novel algorithmic inference method for estimating parameters of bivariate Clayton copulas, addressing specific statistical challenges and demonstrating improved accuracy through numerical experiments.

Contribution

It introduces a new iterative numerical procedure for parameter estimation in copulas, overcoming issues of dependence and lack of sufficient statistics.

Findings

Outperforms existing estimation methods in accuracy

Addresses dependence issues in Kendall statistics

Provides a practical iterative estimation routine

Abstract

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. \alpha. The variant is rooted on a numerical procedure in order to find the \alpha estimate 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.