3 problems

Let $Z_1,Z_2,\ldots,Z_n$ be independent and identically distributed random variables, with each $Z_i$ representing a cluster of $m>1$ observations, and suppose that $c(i)=1$ for al…

Finite-covariance conjecture. Whenever $p$ has finite covariance, a version of the paper’s main theorem holds for some $\epsilon_{n,\delta}(p)$ that approaches the high-dimensional…

High-dimensional sub-Gaussian lower-bound conjecture. Mean estimators cannot outperform this sub-Gaussian rate in the asymptotic regime as $n\to\infty$.