Regression-based local dependence measures

Resumen

In the literature we can find numerous measures that condense the captured informationon the dependence into a single value, which may result in a loss of important detailsabout the dependence relationship. In contrast, local dependence measures o↵er greaterflexibility, enabling us to identify the location, intensity, and direction of dependence acrossvariables. Thus, they allow us to study the behavior of dependence in specific regions ofthe distribution. In this paper, we propose bivariate local regression dependence measuresof Y on X based on the conditional distributionsX|Y >G1(p), for all p 2 (0, 1),which capture the regression dependence of Y on X along the rank of Y by means ofthe expectations E ⇥X|Y >G1(p)⇤ for all p 2 (0, 1). Our measures capture the fullspectrum of dependence, ranging from extreme negative dependence to extreme positivedependence, passing through independence.