  In this paper we develop a novel nonparametric framework to test the
independence of two random variables $\mathbf{X}$ and $\mathbf{Y}$ with unknown
respective marginals $H(dx)$ and $G(dy)$ and joint distribution $F(dx dy)$,
based on {\it Receiver Operating Characteristic} (ROC) analysis and bipartite
ranking. The rationale behind our approach relies on the fact that, the
independence hypothesis $\mathcal{H}_0$ is necessarily false as soon as the
optimal scoring function related to the pair of distributions $(H\otimes G,\;
F)$, obtained from a bipartite ranking algorithm, has a ROC curve that deviates
from the main diagonal of the unit square.We consider a wide class of rank
statistics encompassing many ways of deviating from the diagonal in the ROC
space to build tests of independence. Beyond its great flexibility, this new
method has theoretical properties that far surpass those of its competitors.
Nonasymptotic bounds for the two types of testing errors are established. From
an empirical perspective, the novel procedure we promote in this paper exhibits
a remarkable ability to detect small departures, of various types, from the
null assumption $\mathcal{H}_0$, even in high dimension, as supported by the
numerical experiments presented here.
