5 problems

Let $S$ be a set of $n$ points in $d$-dimensional space. The regression depth of a hyperplane is the minimum number of points intersected by the hyperplane as it undergoes a contin…

Let $P$ be a set of $n$ points, and let regression depth be the minimum number of points intersected by a hyperplane during any continuous motion taking it to a vertical hyperplane…

Let $\widehat{\bm{S}}_n$ be the normal-scores covariance and let $\widehat{\bm{\Sigma}}^{\tau}$ be the sin-transformed Kendall matrix. Assume $p/n\to\gamma$. Spectral equivalence o…

Let $\mu$ be a distribution and let $\mathcal{F}[\mu,\psi]$ denote the relevant concentration objective for a coordinate $\psi$. Given $n$ samples, let $\hat{\psi}_n$ be a data-dri…

Let $\mathcal{P}$ be a distribution family on $(0,\infty)$ whose members have power-law tails satisfying $P(X>x)\sim x^{-\alpha}$ for some $\alpha>0$. Let the logarithmic coordinat…