A Copula‐Based Non‐parametric Measure of Regression Dependence

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Measuring Association on Topological Spaces Using Kernels and Geometric Graphs (2020, methodology): “1] where the authors only consider the case d2 = 1 (also see [31]):”
On boosting the power of Chatterjee’s rank correlation (2021, background): “…paper, we make such a revision by encouraging incorporating a diverging M = Mn many right nearest neighbors (NNs) into the construction of the correlation coefficient, which we show is still an almost surely consistent estimator of Dette et al. (2013)’s measure of dependence as long as M/n → 0.”
On Azadkia–Chatterjee’s conditional dependence coefficient (2021, background): “…an earlier introduced measure of marginal dependence between Y and (a random scalar) Z, namely, ξDSS = ξDSS(Y,Z) := ∫ Var { P ( Y ≥ y ∣∣Z )} dPY (y) ∫ Var { 1 ( Y ≥ y )} dPY (y) , (2.2) which Dette et al. (2013) introduced for continuous distributions and Chatterjee (2021) considered in general.”