Estimació de la mitjana: una revisió d'avenços recents

Abstract

Perhaps the most basic statistical problem is to estimate the expected value of a random variable based on independent observations of the same distribution. This seemingly simple question raises surprising difficulties both from a statistical and a computational point of view. In this paper we survey some of the recent advances in mean estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data in both the univariate and multivariate settings. We focus on estimators based on median-of-means techniques, although other methods such as the trimmed mean and Catoni's estimator are also reviewed. We offer detailed evidence for our core findings.