4 problems

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

Diaconis–Perlman unique crossing conjecture. If $\eta\prec\theta$, but $\theta$ is not a permutation of $\eta$, then $F_\eta(x)-F_\theta(x)$ changes signs exactly once, from $-$ to…

Let $\gamma_t$ and $\gamma_s$ be independent gamma random variables with parameters $t,s>0$. The gamma-product conjecture. For all $s,t>0$, the independent product…

Let $n\geqslant2$ and $\textbf{Y}=(Y_1,Y_2,\ldots,Y_n)$ be a vector of i.i.d. random variables. Let $G_a$ denote a gamma random variable with parameter $a$, and let $B_{a,b}$ denot…