A kernel-copula embedding statistic equals zero exactly when causal dependence between X and Y is stable and is strictly positive otherwise, with a near-linear estimator and convergence rates provided.
arXiv preprint arXiv:2010.01768 , year=
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Introduces dependence functions φ_{(Y,X)} and κ_{(Y,X)} that extend Chatterjee's ξ by quantifying geometric concentration of the Markov product near the diagonal.
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Detecting Changes in Causal Dependence with Kernels and Copulas
A kernel-copula embedding statistic equals zero exactly when causal dependence between X and Y is stable and is strictly positive otherwise, with a near-linear estimator and convergence rates provided.
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Dependence functions based on Chatterjee's rank correlation
Introduces dependence functions φ_{(Y,X)} and κ_{(Y,X)} that extend Chatterjee's ξ by quantifying geometric concentration of the Markov product near the diagonal.