4 problems

Uniform asymptotic exactness conjecture. For every $\alpha\in(0,1)$, there is no confidence set that is asymptotically exact uniformly over $\mathfrak{Ber}$ at level $1-\alpha$.

Let $X_1,\ldots,X_d$ be independent Bernoulli random variables with means $\theta_i$, and let … Write $H(\theta)$ for the entropy of $S$ as a function of…

Let $X$ be Bernoulli with $P(X=1)=p=1-q=P(X=0)$, assume $p\geq q$, and constrain the independent noise $Y$ by $\operatorname{var}(Y)\leq\varepsilon$. For sufficiently small…

We consider Bernoulli bandit models with two arms, whose means satisfy $(\mu_1,\mu_2)\in(0,1)^2$ and $\mu_1\ne\mu_2$. In the fixed-confidence setting, a sampling strategy is non-un…