In light-tailed settings, mean estimation is synonymous with concentration, since the sample-mean is the natural estimate of the mean and we’re usually interested in concentration of the sum or mean of random variables. In heavy-tailed settings this is not the case, as the sample mean is a suboptimal estimate of the mean.
So here we ask what we can say about the sample mean, and we discuss scalar heavy-tailed mean estimation and multivariate heavy-tailed mean estimation elsewhere.
Truncation+Chernoff
Hanh & Klass (1997, AoP). todo