5 problems

Let $\mathscr{E}_1,\dots,\mathscr{E}_n$ be independent exponential random variables, and consider weighted sums of their centered versions,…

Let $\mathscr{E}_1,\mathscr{E}_2,\dots$ be independent exponential random variables, let $G\sim N(0,1)$, and let $p_0$ be the crossover parameter used in the paper. Consider all fi…

Let $n$ be a fixed even positive integer, let $p\geq 2$, and let $X=\sum_{j=1}^n x_j\mathscr{E}_j$, where the $\mathscr{E}_j$ are independent exponential random variables and…

Failure conjecture. The condition

Exponential dilatation conjecture. The sequence $(\alpha_n^{\theta^{\star},0})_{n\geq 1}$ is asymptotically $L^s$-optimal. Numerical experiments for an exponential distribution sup…