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Thursday, February 3, 2022

**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 first talk I will elaborate on this problem; present several other estimators such as median-of-means, Catoni’s estimator, and Trimmed median; and prove some basics results about them. My talks will be based on the survey paper by Lugosi and Mendelson https://arxiv.org/abs/1906.04280. Here is a zoom link: https://illinois.zoom.us/j/84500990503?pwd=Szhhb0xIUktoM2wxQ29xaERmUVpMZz09.

Thursday, February 10, 2022

Thursday, February 17, 2022

Thursday, February 24, 2022

Thursday, March 3, 2022

Thursday, March 24, 2022

Thursday, March 31, 2022

Thursday, April 7, 2022

Thursday, April 14, 2022