Mathematics

Robust Mean Estimation (part 2)

Greg Terlov (UIUC Math )

Abstract: One of the most fundamental problems of statistics is to estimate the expected value of a random variable given $n$ i.i.d. samples. It is natural to do so by considering the empirical mean, however when one works with heavy-tailed distributions empirical mean would give less than ideal accuracy and confidence intervals for finite $n$ and thus one has to consider other estimators. In the last talk we saw that taking median-of-mean yields promising results in 1 dimension but the construction depends on the given confidence interval. In this talk we will discuss this dependency and show that it cannot be improved without further assumptions on the distributions. Following that we will discuss how to extend this procedure to a multidimensional setting. These talks are be based on the survey paper by Lugosi and Mendelson https://arxiv.org/abs/1906.04280.