The attainable (ξ, ρ) region is a convex set with boundary from novel diagonal-band copulas; ξ ≤ |ρ| holds under stochastic monotonicity and the maximum of ρ − ξ equals 0.4.
A simple extension of azadkia and chatterjee’s rank correlation to a vector of endogenous variables
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Introduces dependence functions φ and κ that extend Chatterjee's ξ-coefficient by quantifying both functional dependence and concentration of the Markov product near the diagonal.
Causality-encoded diffusion models use a known DAG to train graph-consistent conditional diffusions for observational recovery, interventional sampling via fixed-variable propagation, and a resampling-based directed edge test with convergence rates depending on local dimension.
Closed-form expressions are derived for association measures of approximating copulas including Chatterjee's ξ, with a proof that ξ(C_n) ≤ ξ(C) and convergence as n→∞ for TP2 copulas under checkerboard approximation.
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