15 problems

Tight measurement complexity conjecture. The lower bound can be extended to every

Let an additive global Fréchet regression estimator use an elastic-net-type penalty within a reproducing kernel Hilbert space framework, and consider debiasing techniques analogous…

Let $\mathcal{S}$ be the central subspace and let the hierarchical prior assign mass to subspaces of varying dimension, including dimensions greater than the intrinsic dimension…

Let thresholded SCAD denote the smoothly clipped absolute deviation variable-selection method followed by a thresholding post-processing step, and let $\rho$ denote the relevant po…

Optimal tuning parameter conjecture. Based on simulation results, the DPD-SIS with an $\alpha$ value around $0.3$ performs the best in the case of dependent covariates.

The paper considers a DPD loss function and a covering-number assumption on the spaces $\Gamma_j$ used in Lemma $\mathrm{L2}$. DPD-loss extension conjecture. It should be possible…

Consider variable-selection problems with estimator collections and minimal-penalty algorithms, including settings beyond orthonormal variable selection and change-point detection.…

Consider variable selection with an orthonormal design and Gaussian noise, with $D_m$ denoting model dimension and $\sigma^2$ the noise variance. In this setting, the minimal penal…

Let $a$ denote the signal amplitude, $\sigma$ the noise level, $s$ the sparsity, $p$ the ambient dimension, and $n$ the sample size. Assume that … For a sufficiently small constant…

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…

Let $\lambda_k$ be the tuning parameter associated with the covariate coefficient $\beta_k$, and let the standard error of $\beta_k$ denote its estimated sampling uncertainty. Li–L…

Let $\mathbf{M}_{n(O)}$ be the matrix formed using the first $q$ variables for the exact oracle sparse dimension-reduction estimator, and let $\mathbf{M}_{n(q)}$ be the correspondi…

The leukemia dataset contains gene-expression measurements for 72 patients classified as acute lymphoblastic leukemia or acute myeloid leukemia, including the Zyxin, Transcriptiona…

Let $\lambda_j$ be the smoothing or penalty parameter associated with the $j$th component, and let $\beta_j$ be the corresponding regression parameter. The unpenalized maximum pseu…

Single-index distribution conjecture. The results of the paper should continue to hold under this assumption, without specifying the conditional distribution beyond its dependence…