Leírás
Abstract:
Recently, motivated by advances in machine learning and data science, there is a great interest in statistics to construct mean estimates that can achieve high accuracy with a large confidence - with possibly wide tailed distributions. As an introduction we discuss some of the recent progresses on the accuracy versus confidence tradeoff in the quite well understood univariate case. After presenting the basic ideas of how to measure the quality of an estimator and the notion of optimality in the sense of sub-Gaussian performance we enumerate possible approaches how to construct an estimator better then the empirical mean - with special attention on the simple but powerful methodology based on median-of-means techniques. Then, we focus our attention to a recent result by Gábor Lugosi and Shahar Mendelson that focuses on the estimation of the mean of a random vector. An extension of the above mentioned technique, the multivariate median-of-means estimator, will be presented and corresponding results will be discussed in great detail.
For Zoom access please contact Miklos Rasonyi (rasonyi.miklos[a]renyi.hu).