Ambrus Tamás (SZTAKI and ELTE): Data-Driven Confidence Intervals for the Mean of Heavy-Tailed Distributions

Estimating the expected value is one of the key problems of statistics, and it serves as a backbone for countless methods in machine learning. In this talk I present a new algorithm to build non-asymptotically exact confidence intervals for the mean of a symmetric distribution based on an independent, identically distributed sample. The method combines resampling with median-of-means estimates to ensure optimal subgaussian bounds for the sizes of the confidence intervals under mild, heavy-tailed moment conditions. The scheme is completely data-driven: the construction does not need any information about the moments, yet it manages to build exact confidence regions which shrink at the optimal rate.