Tuesday, August 24, 2021
Quantitative Methods Research Seminars: Prof. Stanislav Minsker, Dep. of Mathematics, University of Southern California
Let X be a random variable with unknown mean and finite variance. We discuss estimators of the mean of X that are (a) robust with respect to the possible presence of outliers in the sample, (b) provide tight sub-Gaussian deviation guarantees without any additional assumptions on the shape or tails of the distribution, and (c) are asymptotically efficient, meaning that such estimators “extract" all useful information about the parameter of interest available in the sample. One estimator possessing such qualities is constructed using the novel approach based on the properties of self-normalized sums. Another method is based on the permutation-invariant version of the well known “median-of-means” estimator. These are the first estimators that provably combine properties (a), (b) and (c) in one package. Finally, we will discuss applications of presented ideas to robust empirical risk minimization.
Parts of the talk are based on a joint work with M. Ndaoud.