Beyond Catoni: Sharper Rates for Heavy-Tailed and Robust Mean Estimation

Shivam Gupta, Samuel B. Hopkins, Eric Price

We study the fundamental problem of estimating the mean of a $d$-dimensional distribution with covariance $\Sigma \preccurlyeq {\sigma }^2{I}_d$ given $n$ samples. When $d=1$, \cite{catoni} sho…