Leírás
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. Joint work with Szabolcs Szentpéteri and Balázs Csanád Csáji.