3 problems

Let $\mathcal C(\sigma_{\min},\sigma_{\max})$ be the bounded-spectrum correlation class, and let $\widehat{\bm{\Sigma}}$ estimate the latent correlation matrix $\bm{\Sigma}$. Sharp…

Let $p,q>0$ be distinct exponents, and for each $r>0$ let $\mathcal{L}_r$ be the class of losses whose local behavior near $a=\theta$ is $c(\theta)|\theta-a|^r+o(|\theta-a|^r)$ wit…

Let $X\subseteq\mathbb{R}^n$ be a centrally symmetric convex body, let $R(X,\sigma)$ denote its minimax risk, and let $z_{c,k}(X)$ denote the approximation-radius quantity defined…