Estimating copula measure using ranks and subsampling: a simulation study

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 p, q ≤ n, the density in (p/n, q/n) is estimated as 1 mn Pm s=1 Pn i=1 {Ri,s=p,Si,s=q} where Ri,s (respectively Si,s) is the rank in X (resp. Y ) of the i observation of the s sample. 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.