8 problems

Prasad–Takloo-Bighash conjecture. If $\pi$ is $(H,\chi^{-1})$-distinguished, then the Langlands parameter of $\pi_0$ takes values in $\operatorname{GSp}_{2n}(\mathbb{C})$ with simi…

Let $\bm\delta$ be the differential regression parameter and let $\bm\Sigma$ be the covariance matrix. Define … The authors also consider…

MOCE rate lower-bound conjecture. The rate

General consistency theorem conjecture. A general consistency theorem under the global null for linear models should hold, and proving it may require a general version of Doob's th…

Single-path-faithfulness conjecture. The single-path-faithfulness assumption is satisfied for all linear models.

Suppose that the observed data follow the Gaussian linear model … where $\boldsymbol{\beta}\in\mathbb{R}^d$ is an unknown, potentially dense signal, the rows of $X$ are independent…

Effective signal-to-noise ratio estimation conjecture. It may be possible to derive effective estimators of $\eta^2$ when $d \geq n$, provided $\sup d/n < \infty$.

Let $\delta^H$ and $\delta_U$ denote the generalized Bayes estimators corresponding to $a=2$ and $a=p$, respectively, and let $\delta^{GB}_a$ be the generalized Bayes estimator ind…