15 problems

Nešlehová's conjecture. Multidimensional directional $\rho$-coefficients can be expressed as a linear combination of lower-dimensional directional coefficients.

Diagonal-coupling conjecture. The supremum

Multivariate population-limit conjecture. The convergence

Let $(\mX,Y)$ be the random pair underlying the rank-based Azadkia–Chatterjee statistic $\xi_n$, and let $\sigma_2^2$ denote the variance term appearing in the paper's limiting dis…

The tau–rho region conjecture.

Let $(X_1,Y_1),(X_2,Y_2),\ldots$ be a random sample from $(X,Y)$, let $E_n$ be the empirical object used in the estimator, let $N(n)$ be the resolution chosen as in the paper, and…

Let $X$ and $Y$ be random variables, and suppose that the distribution $\mu_Y$ of $Y$ has non-trivial atoms: sets $A$ with $\mu_Y(A)>0$ such that every subset $A'\subset A$ satisfi…

Let $I$ be the AUK-based dependence index for a random vector, and let…

Let $X$ and $Y$ be Banach-space-valued random variables, and let $\mathop{\mathrm{eCor}}$ denote earth mover's correlation. The full earth mover's correlation axiom conjecture. Und…

Non-sharpness conjecture. In the class of extreme-value copulas, the upper Hutchinson–Lai inequality is not sharp either. The paper proves that the lower Hutchinson–Lai inequality…

Let $X,Y$ be continuous random variables such that $Y$ is stochastically increasing in $X$ and $X$ is stochastically increasing in $Y$. Their Kendall's $\tau$ and Spearman's $\rho$…

Let $\tau_P^*(X,Y)$ denote the multivariate partial $\tau^*$, obtained from the rank indicator $I_P$ and the alternating kernel $H_{\tau^*}$. A dependence measure is D-consistent w…

For bivariate random variables $X$ and $Y$, let $\tau^*(X,Y)$ denote the Bergsma–Dassios sign-covariance defined through concordant and discordant quadruples. Bergsma–Dassios' cons…

Let $X$ and $Z$ be random variables with a joint density with respect to Lebesgue measure. The quantities $\nu^{-1}$ are regression-based measures of dependence, and $I(X;Z)$ denot…

Unit star-norm conjecture. The copulas with unit $*$-norm are exactly those whose supports have Lebesgue measure zero in $[0,1]^2$.