12 problems

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

Multivariate population-limit conjecture. The convergence

For two probability measures … , define $\preceq_{\texttt{MCH}}$ when there is a finite sequence of elementary operations transforming … . Let $U_d$ be the sign-vector space, let…

Quasi-copula patching conjecture. Under the condition that the volume $V$ of $R$ is nonzero, the desired patch is equal to

Let $\mathbf{X} \in \mathbb{R}^k$ be a random vector, and let its Fréchet $p$-mean be … Here $\|\cdot\|$ is the Euclidean norm. Define the unit tangent vector to the trajectory of…

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

Let … be the related family of test statistics obtained by replacing the theoretical characteristic function in $T_{n,a}$ with its empirical counterpart. Analogue conjecture for…

Low-rank prediction conjecture. It is always desirable to use reduced rank multivariate kernel ridge regression when the underlying function $F$ is of low rank.

Depth characterization conjecture. For any two distinct probability distributions $P$ and $Q$ on $\mathbb R^d$, there exists a point $x\in\mathbb R^d$ at which the depths $D(x;P)$…

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…

Influence-function conjecture. The influence function of the proposed estimator is the same as the influence function of the S-estimator for complete data.

Let $C$ be a multivariate copula, and let $\Sigma$ be the covariance matrix associated with the estimators in the paper. A bivariate margin of $C$ is the copula obtained by restric…