9 problems

Let $F_{n,2}^{G,L}(t)$ denote the largest-eigenvalue distribution function for the Gaussian unitary ensemble or Laguerre unitary ensemble under the scaling in the preceding expansi…

Let $B\geq 1$ be fixed, let $\nu$ be a positive integer, and let $\mathsf q\in\mathbb R$. Let $\Psi_B$ and $\psi_B$ denote the distribution function and density function, respectiv…

Let $W_p$ denote the Wasserstein distance of order $p$, with $p>1$. Higher-order Wasserstein extension conjecture. Theorem should extend to $W_p$ for $p>1$, at least for i.i.d. seq…

Edgeworth expansions concern asymptotic refinements for estimators in nonparametric regression, and the uniform kernel is the kernel $K(u)=\mathbbm{1}\{|u|<1\}/2$. Hall's conjectur…

Non-Gaussian fixed-smoothing expansion conjecture. Under fixed-smoothing asymptotics, the leading error term in the expansion of its distribution function involves the third- and f…

Non-Gaussian error-rate conjecture. In the non-Gaussian case, the leading error term has order

Let $T_N$ be the Studentized trimmed mean considered above, and let assumption (1.18) of Putter and van Zwet consist of its first and second conditions. The authors' conjecture. Th…

Conjecture on removing condition [L]. Both $(\mathrm{EE\_n2})$ and $(\mathrm{EE\_s2})$ should remain valid without condition $[L]$.

Exact-order conjecture. Under some regularity assumptions, the exact order of this approximation is $k^{-3/2}$.