7 problems

The Letac–Massam conjecture.

Let $d\geq 2$, let $p<\frac{d-1}{2}$, and let $\omega$ be the non-centrality parameter of a non-central Wishart distribution. Mayerhofer's rank conjecture. In this case, the non-ce…

Let $W$ be distributed as $\operatorname{Wishart}_p(2\alpha,\Sigma/2)$, where $2\alpha\in\mathbb{N}\cup(p-1,\infty)$, $\Sigma$ is a $p\times p$ symmetric positive definite matrix,…

Let $\mathcal{S}$ be the operator associated with the goodness-of-fit problem for the Wishart distributions, and let $\mathcal{S}_0$ denote the corresponding null operator. Distinc…

Let $\mathcal{S}_p=\operatorname{Sym}(\mathbf{R},p)$ be the space of symmetric $p\times p$ matrices, let $\mathcal{S}_p^+$ be the open cone of positive definite matrices, and let…

Strengthened rank bound conjecture. The non-centrality parameter should satisfy

Let $d\geq 2$. For parameters $p\geq 0$, scale matrix $\sigma$, and non-centrality parameter $\omega$, consider the Wishart distribution characterized by the Laplace transform … He…