6 problems

Optimal augmentation-size conjecture. Under this regime,

Consider the oracle procedure In-sample BH and the non-oracle procedure CRT + BH in the multivariate normal means testing problem. Both procedures produce $p$-values, and their exp…

Let $\tilde m_{\textnormal{opt}}$ be the choice of augmentation size that maximizes the power of BONuS for a point-mass prior, with $m$ fixed. Optimal augmentation-size conjecture.…

Adaptive weighted test power dominance conjecture. The power of $\phi_{\textnormal{wtd+}}$ dominates that of $\phi_{\textnormal{wtd}}$ across the full range of signal strengths.

Consider the pointwise regression testing problem described above, with conditional variance function $sigma(x)$, covariate distribution for $X_i$, smoothness parameter $beta$, rad…

Adaptivity conjecture. The ideas of adaptivity should be developable for the multivariate nonparametric regression models considered in this paper, although the exact details requi…