content_image/326978.jpg
<img src='content_image/326978.jpg'>

## H Simulations of monotone relationships 

Four monotone relationships are presented in Figure 12. Figure 13 shows that the differences for the summation variants between ADP and DDP are negligible, and that the power decreases with m for all of these variants. Similar conclusions hold for the maximum variants in Table 10. Table 10 further shows that for a linear relationship, Pearson, Spearman, Hoeffding and dCov are clearly superior, but for the remaining three monotone relationships min$_{m}$$_{∈{}$$_{2}$$_{,...,m}$$_{max}$$_{}}$ p$_{m}$ has quite good power properties. 

## I Comparisons of dCov/HHG on ranks and on data 

In Section 4 we only considered distribution-free competitors. Therefore, we applied dCov and HHG on ranks rather than on data, even though they were designed as permutation tests on data. Usually, the computational advantage of performing the 

