14 problems

Linear worst-case FDR conjecture. There exists a universal constant $C>0$ such that, for every nominal level $q$, the worst-case FDR is at most $Cq$.

BH FDR control conjecture. For every $q\in(0,1)$, every $N\in\mathbb N$, every $\theta\in\mathbb R^N$, and every correlation matrix $\Sigma$, the Benjamini--Hochberg procedure sati…

Equivalence conjecture. The compound $\overline{\operatorname{eBH}}$ procedure and the standard compound eBH procedure are equivalent, so that

The paper studies approximate knockoffs generated by matching the first two moments of covariates, with dimension $p$ and sample size $n$. In the heavy-tailed setting, the theory r…

The two-group mixture model has independently drawn hypothesis labels, with each hypothesis non-null with probability $pi_1$. In the fixed non-null model, the number of non-null hy…

Let $n,d\to\infty$ with $n/d\to\delta$, let $K=K_n\to\infty$ and $\varepsilon=\varepsilon_n\to0$ slowly enough. Suppose that, for every $m\in[M]$, $\widehat\Pi_{-m}$ converges weak…

Let $n,d\to\infty$ with $n/d\to\delta$, let $K=K_n\to\infty$ and $\varepsilon=\varepsilon_n\to0$, and assume the Bayesian linear model of Assumption. Let $\boldsymbol T_\star$ be e…

Limiting FDP and TPP conjecture. The limiting false discovery proportion and true positive proportion of TPoP satisfy

Conjecture on faster dimensional growth. Similar theoretical results for the RESS and refined RESS methods should also hold when

Let $W_j$ denote the knockoff statistics used in the AKO+BH procedure, and suppose that Assumption … can be relaxed to some mixing condition. The conjecture is motivated by the fac…

Weak-dependence extension conjecture. Similar theoretical results should also hold when $varepsilon_i$ and $\mathbf{f}_i$ exhibit sufficiently weak serial dependence.

The knockoff procedure is applied to high-dimensional controlled variable selection, with covariates potentially modeled or clustered and a statistic used to identify discoveries w…

Finner et al.'s conjecture. A least favorable configuration for the FDR of the LSU is still the Dirac-uniform distribution.

Let $\mathbf{\delta}_F^*$ denote the multiple decision function introduced in the paper, and let the size condition be the condition imposed on the multiple decision size vector to…