7 problems

Misspecified Cramér–Rao bound conjecture. The mean-square error satisfies

Let $\mathscr{L}$ be a rich loss space, for example the space of all continuous losses satisfying mild growth conditions, and let optimality be defined by a natural optimality noti…

Let $\mu$ be a distribution on $\mathbb{R}$, and consider estimators for the associated location family. An estimator is shift-invariant if shifting every observation by $c$ shifts…

One-sided estimation lower-bound conjecture. There exist constants $c_0,c,r>0$ such that, for every $s,n\in\mathbb{N}$ satisfying

Let $P$ be the probability measure and let $\bar P$ be its Wasserstein barycenter. Let ${\bar P}_n$ denote the empirical Wasserstein barycenter based on $n$ observations, and let…

Nonexistence conjecture. There is no estimator $\mathscr T$ satisfying this equation when both $\kappa_1$ and $\kappa_2$ are unknown.

Let $X(1),\ldots,X(n)$ be a sequence of consecutive increments, or alternatively let $W(1),\ldots,W(n)$ be observed workloads, and let $\theta^*$ denote Loynes' exponent. Consider…