6 problems

Two-block-design sufficiency conjecture. A single block design is not sufficient to attain the optimal PUT, whereas the two block designs with $k=1$ and $k=2$ are sufficient to att…

Let $\mathsf{t_{mix}}$ denote the mixing-time parameter of the stationary $\alpha$-mixing stochastic process, and let the estimator be the one introduced in the paper for estimatin…

Let $p=p_{i\in\mathbb{N}}$ be any distribution on $\mathbb{N}$, let $\tilde p$ be an arbitrary estimator based on $n$ observations, and let $V^*(p)$ denote the population variance-…

Let $p=p_{i\in\mathbb{N}}$ be a distribution over $\mathbb{N}$, let $\hat p$ be its maximum-likelihood estimator, and define … Write $V^*$ and $\hat V^*$ for the corresponding popu…

Non-interactive lower-bound conjecture. The local lower bound in Theorem4 cannot be achieved by any non-interactive scheme.

Unconditional lower-bound conjecture. Theorem 1 should remain valid without this assumption. The assumption is used to obtain lower bounds for adaptive estimators based on reasonab…