4 problems

Brown's conjecture. The prior $g(\theta)$ leads to an admissible estimator, regardless of the density $p$ and the loss function $W$.

Let $E_k$ be the simplex of multinomial probability parameters, let … and, for $R\geq 1/k$, let … For $R\in(1/k,1)$, choose $j$ such that … where $\nu_j=\sqrt{\frac{j}{k(k-j)}}$ is…

Let $\widetilde{\beta}_{N}$ be the Bayesian estimator considered above, and let $\varrho\in\mathcal{Q}_{e,2}$ be a prior. Asymptotic-efficiency conjecture. The asymptotic efficienc…

Let $B_t$ denote the information matrix at time $t$, let $B^*$ be the optimal limiting information matrix, and let $\operatorname{Cov}_t(\Theta)$ denote the posterior covariance of…