5 problems

Inner-loop error-bound conjecture.

Let $1<p<\infty$, and let $U=\{u_k\}$ be an exponential-function family in $L^p(0,1)$, with the distance between normalized exponential-function families defined by the displayed q…

Uniqueness conjecture. The map

Nonnegativity conjecture for Riesz kernels. For $\alpha\gg 0$, the Riesz kernel $q_\alpha(\sigma)$ takes nonnegative values on $K$.

Let $N$ be the size of the finite sample space and let $k$ be the dimension of an exponential family. For a class $\mathcal{H}$ of exponential families, define … In particular, let…