Estimating copula measure using ranks and subsampling: a simulation study

TL;DR

This paper introduces a novel subsampling and ranking-based method for estimating copula measures, which avoids kernel selection and demonstrates improved performance over traditional kernel methods in simulations.

Contribution

The paper presents a new copula estimation technique using subsampling and rank counting, simplifying the process by eliminating kernel choice and focusing on subsample size.

Findings

Method outperforms kernel-based estimators in simulations

Avoids kernel selection and tuning

Reduces complexity to choosing subsample size

Abstract

We describe here a new method to estimate copula measure. From N observations of two variables X and Y, we draw a huge number m of subsamples (size n<N), and we compute the joint ranks in these subsamples. Then, for each bivariate rank (p,q) (0<p,q<n+1), we count the number of subsamples such that there exist an observation of the subsample with bivariate rank (p,q). This counting gives an estimate of the density of the copula. The simulation study shows that this method seems to gives a better than the usual kernel method. The main advantage of this new method is then we do not need to choose and justify the kernel. In exchange, we have to choose a subsample size: this is in fact a problem very similar to the bandwidth choice. We have then reduced the overall difficulty.