8 problems

Given observations $\mathbf x=(x_1,\dots,x_n)$, define … where the observations are independent e-values. Gaffke's conjecture. The quantity $K_n(\mathbf x)$ is a valid $p$-value wh…

Equivalence conjecture. The compound $\overline{\operatorname{eBH}}$ procedure and the standard compound eBH procedure are equivalent, so that

Nonsymmetric e-merging conjecture. Every admissible e-merging function, without assuming symmetry, should be a convex combination of a weighted average and the constant $1$.

Let $\mathcal{P}^{\rm mar}$ and $\mathcal{Q}^{\rm mar}$ be the marginal null and alternative families, with $\mathcal{P}=\{P^\infty:P\in\mathcal{P}^{\rm mar}\}$ and…

Let $\mathcal{P}$ and $\mathcal{Q}$ be families of probability measures on $\mathfrak{X}$. Suppose there exist $P_0\in\mathcal{P}$ and $Q_0\in\mathcal{Q}$ such that $P\ll P_0$ for…

Let $\mathcal{P}$ and $\mathcal{Q}$ be the null and alternative families in the paper, and for each $n$ let $\ell_n$ be the maximum e-power among pivotal and exact e-variables for…

Let $\Theta$ be an index set, and let $\{P_i,Q_j\}_{i,j\in\Theta}$ be probability measures on $\mathfrak{X}$. Suppose there is some $\theta\in\Theta$ such that $P_i\ll P_\theta$ an…

Let ${{S}_{\textsc{gro}({{\cal M}})}}$ be the e-variable based on the reverse information projection (RIPr) of a fixed simple alternative onto the null set…