HHG (A consistent multivariate test of association based on ranks of distances) is introduced in:
Heller, R., Heller, Y., & Gorfine, M. (2012b). A consistent multivariate test of association based on ranks of distances. Biometrika, arXiv preprint arXiv:1201.3522.
Newer version available here: HHG.
Assuming I can calculate test statistics T(X,Y), where $X \in \mathbb{R}^{N\times p}$, $Y \in \mathbb{R}^{N\times q}$ how do I transform it to [0,1] ?
I suppose $N_{sim}$ simulations are required to get $T_i(X,Y_{perm,i})$, where $Y_{perm,i}$ is Y with randomly permuted rows (?) and $i \in \{1,N_{sim}\}$, to calculate the correlation (maybe association is a batter term?) ($\in$[0,1]) and p-value? I calculate p as the (number of $T_i>T$)/$N_{sim}$, is that correct ?
The method described at the end of the question above (of calculating Nsim permutations) is indeed the standard way of calculating a p_value for a permutation test such as ours. In fact our R package calculates the p_value this way, so you dont need the perform the permutations yourself. In order to get the p_values please set the parameters as follows: is.sequential = F nr.perm = Nsim
We output four p_values of four variants of the score. The p_value for the most popular statistic can be found in perm.pval.hhg.sl. For more information on the package, please see the manual at http://cran.r-project.org/web/packages/HHG/HHG.pdf. Note, that this number is a p_value and does not have any other meaning as a correlation measure